Abelian Groups - László Fuchs [Springer]

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Author Index 733 Grinshpon, S.Ya., 508, 589, 595 de Groot, J., 85, 125, 126, 147, 437, 438 Gruson, L., 117–119 H Haimo, F., 418, 681 Hajós, G., 86–90 Hales, A.W., 351, 355, 358, 360, 361, 363 Hallett, J.T., 667, 670, 671 Halperin, I., 691, 692 Harrison, D.K., 220, 222, 242–244, 278, 281, 282, 287–289, 291, 293 Hauptfleisch, G.J., 633 Hausen, J., 79, 111, 112, 627, 649, 650, 663, 664, 696, 697 Head, T.J., 237, 323, 325 Heinlein, G., 496 Hensel, K., 704 Herbera, D., 582 Herden, G., 437, 697 Higman, G., 700 Hill, P., 26, 28, 31, 96, 98, 104, 105, 109, 116, 119, 122, 126, 152, 180, 219, 250, 270, 293, 301, 306, 322–325, 329, 338–342, 350, 352–354, 358, 360–364, 368, 369, 373, 376–379, 381, 382, 384, 385, 392, 401–403, 404, 419, 422, 430, 458, 507, 508, 513, 536, 537, 545, 550, 551, 563, 568, 604, 628, 658, 663, 664, 681 Hiller, H.L., 293 Hirsch, K.A., 667, 670, 671 Hjorth, G., 478 Hodges, W., 121, 122 Höfling, B., 417 Hofmann, K.H., 205, 206 Honda, K.Y., 5, 86, 153, 154, 401, 402, 469 Hopkins, C., 688 Huber, M., 269, 275, 285, 286, 293, 407, 495, 508, 513, 518, 649 Hulanicki, A., 187, 222, 437 Hunter, R.H., 351, 370, 422, 429, 461, 588, 601, 604, 605 Huynh, D.V., 139, 688 I Irwin, J.M., 53, 105, 118, 129, 155, 172, 178, 180, 281, 301, 315, 321, 323, 325, 330, 341, 351, 365, 370, 372, 373, 376, 377, 386, 391, 392, 395, 396, 399, 400, 495, 507, 592, 652 Ivanov, A.V., 66, 68, 211, 341, 508, 513, 627, 642, 649 J Jackett, D.R., 680, 681, 692 Jacoby, C., 605 Janakiraman, S., 153 Jans, J.P., 129, 650 Jarisch, R., 605 Jech, T., 124, 312, 330, 332 Jenda, O.M.G., 298 Jensen, C.U., 64, 280, 292 Jensen, R., 23, 24 Johnson, J.A., 627, 696 Johnson, R.E., 137, 139 Jónsson, B., 207, 210, 211, 319, 415, 445, 458, 462, 464, 469 Joubert, S.V., 579 K Kakutani, S., 223 Kamalov, F.F., 111 Kanamori, A., 437 Kaplansky, I., 52, 79, 84, 85, 99, 111, 153, 172, 189, 191, 192, 194–196, 198, 300, 302, 307, 309, 345, 350, 351, 427, 430, 438, 455, 469, 582, 595, 624, 625 Karpenko, A.V., 642 Karpilovsky, G., 700 Kasch, F., 642 Kaup, L., 125 Kechris, A.S., 478 Keef, P.F., 69, 180, 248–251, 326–328, 341, 389, 391, 392, 400 Keller, O.H., 90 Kemoklidze, T., 298, 317 Kertész, A., 37, 111, 139, 142, 143, 145, 431 Khabbaz, S.A., 140, 156, 179, 180, 331, 652, 664 Kiefer, F., 376 Kil’p, M.A., 138 Kleane, M.S., 125 Koehler, J., 414, 535 Kogalowski, S.R., 705 Kojman, M., 589 Kolettis, G., Jr., 350, 375, 376, 426 Kompantseva, E.I, 681 Kovács, L., 170 Koyama, T., 321, 323 Kozhukhov, S.F., 464 Kravchenko, A.A., 422, 430, 541
734 Author Index Król, M., 512, 513, 670 Kruchkov, N.I., 500 Krylov, P.A., 165, 415, 464, 475, 479, 488, 508, 589, 595, 613, 620, 633, 645, 649 Kulikov, L. Ya., 20, 53, 94, 97, 147, 149, 155–157, 159, 167, 171–175, 293, 303, 305, 306, 311, 312, 316, 318, 320, 330, 350, 365, 370, 427, 430, 578 Kurosh, A.G., 96, 146, 305, 415, 436 L Lady, E.L., 324, 430, 446, 448, 457, 458, 465, 467, 469, 476, 478, 534, 535 Lane, M., 458, 611 Lausch, H., 253 Lawrence, J., 123, 126 Lawver, D.A., 621, 681 Lazaruk, J., 400 Lee, W.Y., 536 Lefschetz, S., 224 Leistner, K., 605 Leptin, H., 197, 199, 315, 316, 321, 660, 663 Levi, F.W., 415, 436, 578, 628 Liebert, W., 622, 625, 627, 633, 650, 663 Linton, R.C., 377, 384, 391 Loonstra, F., 440, 443, 445, 469 Łoś, J., 48, 67, 164, 183, 189, 489, 492, 495, 511, 513 Loth, P., 206, 604, 605 Lyapin, E.S., 422 M Mackey, G.W., 345, 350, 595 MacLane, S., 13, 35, 255, 260, 261, 268, 422, 539 Mader, A., 38, 159, 475, 529, 534, 535, 567, 578, 642, 649, 663, 664, 696 Magidor, M., 120, 437, 566, 568 Mal’cev, A.I., 415, 436, 670, 705 Maranda, J.M., 164, 165, 183, 189, 199, 200 Martinez, J., 528 Matlis, E., 139, 286 May, W., 351, 376, 620, 627, 628, 652, 670, 673, 700, 705 McCoy, N.H., 5 Meehan, C., 628 Megibben, C.K., 104, 105, 152, 188, 227, 270, 301, 306, 316, 317, 322–329, 339, 377, 385, 390, 391, 401–405, 407, 430, 458, 507, 508, 536, 584, 586, 587, 589–591, 594–596, 604, 611, 628, 653, 664 Meinel, K., 570 Mekler, A.H., 114, 119–121, 198, 281, 341, 342, 405–407, 437, 475, 494–496, 506–508, 527, 528, 651 Melles, G., 478 Menegazzo, F., 642 Metelli, C., x, 415, 508, 509, 536, 539, 554, 569, 571, 572, 632, 633 Mez, H.C., 681 Mikhalëv, A.V., 613, 620, 628, 645, 649 Mines, R., 396, 536 Minkowski, H., 86, 90 de Miranda, A.B, 671 Mishina, A.P., 139, 154, 510, 512, 513, 579, 620, 660 Missel, C., 400 Misyakov, V.M., 589, 642 Misyakova, A.V., 642 Mohamed, S.H., 139 Mollov, T.Zh., 700 Monk, G.S., 211, 227, 333, 627 Moore, J.H., 604 Morris, S.A., 206 Moskalenko, A.I., 269, 298 Müller, B.J., 139 Müller, E., 416 Murley, C.E., 463–465, 476, 476, 618 Mutzbauer, O., 172, 414–416, 445, 475, 605 Myshkin, V.I., 586, 594, 595 N Nachev, N.A., 700 Nedov, V.N., 670 Neumann, B.H., 6 Nicholson, W.K., 211 Niedzwecki, G.P., 649, 650, 680, 705 Nöbeling, G., 125, 126 Noether, E., 8 Nongxa, L.G., 414, 429, 430, 536 Nunke, R.J., 35, 154, 180, 245–250, 270, 276, 280, 282, 304, 369, 371–374, 376, 377, 386, 388, 391–394, 397, 400, 402–404, 407, 495, 497, 498, 501, 503, 508, 527, 574, 575, 628 O Ohlhoff, H.J.K., 579 Ohta, H., 507 Okuyama, T., 153 O’Meara, K.C., 469
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Springer Monographs in Mathematics
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László Fuchs Abelian Groups 123
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Dedicated with love to my wife Shul
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viii Preface to relevant publicatio
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x Preface on abelian groups. The re
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xii Contents 4 Divisibility and Inj
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xiv Contents 7 Whitehead Groups If
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Table of Notations Set Theory ; : s
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Table of Notations xix N .p/: Nunk
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Table of Notations xxi Q A;;A : di
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2 1 Fundamentals is finite, countab
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4 1 Fundamentals Theorem 1.2. In a
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6 1 Fundamentals (8) A superfluous
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8 1 Fundamentals A ! A=K acting as
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10 1 Fundamentals φ G ⏐ ↓ η 0
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12 1 Fundamentals Lemma 2.5 (Snake
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14 1 Fundamentals Exercises (1) Ass
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16 1 Fundamentals non-zero subgroup
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18 1 Fundamentals in Sect. 7 in Cha
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20 1 Fundamentals 4 Sets Since the
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22 1 Fundamentals It might be helpf
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24 1 Fundamentals This is an amazin
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26 1 Fundamentals of subgroups, ind
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28 1 Fundamentals If is an infinit
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30 1 Fundamentals For the proof of
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32 1 Fundamentals C3. Identity. For
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34 1 Fundamentals is exact in D; F
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36 1 Fundamentals 7 Linear Topologi
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38 1 Fundamentals Proof. (We need s
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40 1 Fundamentals For two R-modules
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Chapter 2 Direct Sums and Direct Pr
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1 Direct Sums and Direct Products 4
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2 Direct Summands 51 Proof. If A D
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2 Direct Summands 53 Exercises (1)
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3 Pull-Back and Push-Out Diagrams 5
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4 Direct Limits 57 In this case, A
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4 Direct Limits 59 We now move to t
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5 Inverse Limits 61 for 0 W G ! A
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5 Inverse Limits 63 for every i 2 I
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6 Direct Products vs. Direct Sums 6
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6 Direct Products vs. Direct Sums 6
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7 Completeness in Linear Topologies
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Chapter 3 Direct Sums of Cyclic Gro
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1 Freeness and Projectivity 77 Coro
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1 Freeness and Projectivity 79 Let
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2 Finite and Finitely Generated Gro
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3 Factorization of Finite Groups 87
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3 Factorization of Finite Groups 89
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4 Linear Independence and Rank 91 E
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4 Linear Independence and Rank 93 t
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5 Direct Sums of Cyclic Groups 95 P
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5 Direct Sums of Cyclic Groups 97 s
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6 Equivalent Presentations 99 (5) (
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6 Equivalent Presentations 101 Thes
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6 Equivalent Presentations 103 Equi
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7 Chains of Free Groups 105 For Ded
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7 Chains of Free Groups 107 We can
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7 Chains of Free Groups 109 Hill’
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7 Chains of Free Groups 111 which i
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8 Almost Free Groups 113 (D) Let 0
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8 Almost Free Groups 115 Proof. (a)
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8 Almost Free Groups 117 be done by
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8 Almost Free Groups 119 with. In t
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9 Shelah’s Singular Compactness T
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10 Groups with Discrete Norm 123 Di
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10 Groups with Discrete Norm 125 Ch
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11 Quasi-Projectivity 127 11 Quasi-
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11 Quasi-Projectivity 129 for diffe
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132 4 Divisibility and Injectivity
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150 5 Purity and Basic Subgroups or
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152 5 Purity and Basic Subgroups Pr
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154 5 Purity and Basic Subgroups ge
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158 5 Purity and Basic Subgroups Th
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160 5 Purity and Basic Subgroups ˛
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166 5 Purity and Basic Subgroups 5
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168 5 Purity and Basic Subgroups Le
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172 5 Purity and Basic Subgroups F
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174 5 Purity and Basic Subgroups (H
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176 5 Purity and Basic Subgroups Ma
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180 5 Purity and Basic Subgroups So
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Chapter 6 Algebraically Compact Gro
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1 Algebraic Compactness 185 of the
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1 Algebraic Compactness 187 Na j ;
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1 Algebraic Compactness 189 Here jG
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2 Complete Groups 191 is a Cauchy s
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2 Complete Groups 193 A ⏐ μ A A
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3 The Structure of Algebraically Co
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3 The Structure of Algebraically Co
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4 Pure-Injective Hulls 199 (2) The
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4 Pure-Injective Hulls 201 subgroup
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5 Locally Compact Groups 203 5 Loca
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5 Locally Compact Groups 205 Theore
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6 The Exchange Property 207 Evident
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6 The Exchange Property 209 In the
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6 The Exchange Property 211 to the
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Chapter 7 Homomorphism Groups Abstr
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1 Groups of Homomorphisms 215 (and
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1 Groups of Homomorphisms 217 is an
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1 Groups of Homomorphisms 219 F Not
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2 Algebraically Compact Homomorphis
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2 Algebraically Compact Homomorphis
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3 Small Homomorphisms 225 (3) The a
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3 Small Homomorphisms 227 completio
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Chapter 8 Tensor and Torsion Produc
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1 The Tensor Product 231 with the f
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1 The Tensor Product 233 for matchi
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1 The Tensor Product 235 finitely P
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2 The Torsion Product 237 (6) (a) I
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2 The Torsion Product 239 It is pre
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2 The Torsion Product 241 It remain
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3 Theorems on Tensor Products 243 T
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4 Theorems on Torsion Products 245
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5 Localization 251 (8) (Keef) If A
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5 Localization 253 Exercises (1) If
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256 9 Groups of Extensions and Coto
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300 10 Torsion Groups (A) If C is a
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302 10 Torsion Groups the indicator
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304 10 Torsion Groups 0 −−−
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306 10 Torsion Groups is tantamount
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308 10 Torsion Groups Proof. We hav
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310 10 Torsion Groups (3) Let A be
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312 10 Torsion Groups (C) B is a ba
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314 10 Torsion Groups pure-injectiv
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316 10 Torsion Groups Theorem 3.11
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318 10 Torsion Groups 4 More on Tor
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320 10 Torsion Groups (g) The large
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322 10 Torsion Groups that in torsi
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324 10 Torsion Groups subgroup of B
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326 10 Torsion Groups (c) Homomorph
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328 10 Torsion Groups then Ker con
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330 10 Torsion Groups A class more
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332 10 Torsion Groups with basic su
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334 10 Torsion Groups 8 Valuated Ve
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336 10 Torsion Groups V D A ` B for
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338 10 Torsion Groups Proof. Define
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340 10 Torsion Groups When Socles D
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342 10 Torsion Groups Hill [1] gave
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344 11 p-Groups with Elements of In
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410 12 Torsion-Free Groups is calle
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412 12 Torsion-Free Groups Proof. L
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414 12 Torsion-Free Groups If A is
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416 12 Torsion-Free Groups Exercise
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418 12 Torsion-Free Groups Converse
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420 12 Torsion-Free Groups fa X j a
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422 12 Torsion-Free Groups and 0 !
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424 12 Torsion-Free Groups (ii) If
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426 12 Torsion-Free Groups number o
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428 12 Torsion-Free Groups along B
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430 12 Torsion-Free Groups whenever
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432 12 Torsion-Free Groups If we ha
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434 12 Torsion-Free Groups Then we
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436 12 Torsion-Free Groups (ii) For
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438 12 Torsion-Free Groups (7) (de
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440 12 Torsion-Free Groups it is ro
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442 12 Torsion-Free Groups 1 for `
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444 12 Torsion-Free Groups A D B i
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446 12 Torsion-Free Groups (5) For
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448 12 Torsion-Free Groups Proof. L
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450 12 Torsion-Free Groups local (T
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452 12 Torsion-Free Groups stable r
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454 12 Torsion-Free Groups (3) (War
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456 12 Torsion-Free Groups write x
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458 12 Torsion-Free Groups For thos
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460 12 Torsion-Free Groups A C 1
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462 12 Torsion-Free Groups ˛./.˛
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464 12 Torsion-Free Groups so the s
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466 12 Torsion-Free Groups followed
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468 12 Torsion-Free Groups (i) ther
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470 12 Torsion-Free Groups 11 Duali
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472 12 Torsion-Free Groups Lemma 11
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474 12 Torsion-Free Groups rk p D.A
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476 12 Torsion-Free Groups is proj(
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478 12 Torsion-Free Groups division
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Chapter 13 Torsion-Free Groups of I
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1 Direct Decompositions of Infinite
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2 Slender Groups 489 (6) A torsion-
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2 Slender Groups 491 Example 2.5. T
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2 Slender Groups 493 Proof. From Th
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2 Slender Groups 495 F Notes. The r
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3 Characterizations of Slender Grou
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3 Characterizations of Slender Grou
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4 Separable Groups 501 Exercises (1
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4 Separable Groups 503 where the G
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4 Separable Groups 505 In the follo
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4 Separable Groups 507 c C g D h 2
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5 Vector Groups 509 (7) Show that t
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5 Vector Groups 511 Isomorphism of
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6 Powers ofZ of Measurable Cardinal
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7 Whitehead Groups If V = L 519 (7)
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7 Whitehead Groups If V = L 521 Pro
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7 Whitehead Groups If V = L 523 Sˇ
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8 Whitehead Groups Under Martin’s
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8 Whitehead Groups Under Martin’s
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Chapter 14 Butler Groups Abstract T
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1 Finite Rank Butler Groups 531 and
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1 Finite Rank Butler Groups 533 Pro
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1 Finite Rank Butler Groups 535 Let
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2 Prebalanced and Decent Subgroups
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2 Prebalanced and Decent Subgroups
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3 The Torsion Extension Property 54
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4 Countable Butler Groups 547 (ii)
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5 B 1 -andB 2 -Groups 549 (F) Homog
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6 Solid Subgroups 551 understand th
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6 Solid Subgroups 553 fa n j n
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6 Solid Subgroups 555 Again changin
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7 Solid Chains 557 (4) A corank 1 s
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7 Solid Chains 559 B C1 =B admits
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7 Solid Chains 561 Lemma 7.6 (Bican
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8 Butler Groups of Uncountable Rank
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9 More on Infinite Butler Groups 56
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9 More on Infinite Butler Groups 57
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Chapter 15 Mixed Groups Abstract Mi
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1 Splitting Mixed Groups 575 For ev
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1 Splitting Mixed Groups 577 so A m
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2 Baer Groups are Free 579 (4) (Opp
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2 Baer Groups are Free 581 We note
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2 Baer Groups are Free 583 One does
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3 Valuated Groups. Height-Matrices
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4 Nice, Isotype, and Balanced Subgr
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5 Mixed Groups of Torsion-Free Rank
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5 Mixed Groups of Torsion-Free Rank
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6 Simply Presented Mixed Groups 597
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7 Warfield Groups 599 Exercises (1)
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7 Warfield Groups 601 (i) A=F is to
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7 Warfield Groups 603 Lemma 7.7 (St
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8 The Categories WALK and WARF 605
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8 The Categories WALK and WARF 607
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9 Projective Properties of Warfield
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9 Projective Properties of Warfield
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Chapter 16 Endomorphism Rings Abstr
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1 Endomorphism Rings 615 Lemma 1.5.
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1 Endomorphism Rings 617 For a subg
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1 Endomorphism Rings 619 Before sta
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1 Endomorphism Rings 621 Recently,
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2 Endomorphism Rings of p-Groups 62
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3 Endomorphism Rings of Torsion-Fre
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4 Endomorphism Rings of Special Gro
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5 Special Endomorphism Rings 637 se
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5 Special Endomorphism Rings 639 Pr
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5 Special Endomorphism Rings 641 Re
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6 Groups as Modules Over Their Endo
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7 Groups with Prescribed Endomorphi
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7 Groups with Prescribed Endomorphi
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656 17 Automorphism Groups Example
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658 17 Automorphism Groups linear g
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660 17 Automorphism Groups Exercise
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662 17 Automorphism Groups Accordin
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664 17 Automorphism Groups (2) If A
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666 17 Automorphism Groups (b) If G
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668 17 Automorphism Groups Then a 7
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670 17 Automorphism Groups for all
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Chapter 18 Groups in Rings and in F
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1 Additive Groups of Rings and Modu
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2 Rings on Groups 677 (11) For a ri
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2 Rings on Groups 679 is a subring,
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2 Rings on Groups 681 Beaumont-Lawv
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Page 722 and 723: References Books D.M. Arnold — [A
Page 724 and 725: References 709 D.M. Arnold, R. Hunt
Page 726 and 727: References 711 R. Burkhardt — [1]
Page 728 and 729: References 713 M. Dugas — [1] Fas
Page 730 and 731: References 715 A.A. Fomin — [1] T
Page 732 and 733: References 717 R. Göbel, S. Shelah
Page 734 and 735: References 719 P. Hill, M. Lane, C.
Page 736 and 737: References 721 A. Kertész — [1]
Page 738 and 739: References 723 A. Mader — [1] On
Page 740 and 741: References 725 L.G. Nongxa — [1]
Page 742 and 743: References 727 endomorphism rings.
Page 744 and 745: References 729 G.M. Tsukerman — [
Page 746 and 747: Author Index A Abel, N.H., vii Albr
Page 750 and 751: Author Index 735 O’Neill, J.D., 3
Page 752 and 753: Subject Index A Abelian group, 1 Ab
Page 754 and 755: Subject Index 739 homomorphism, 37,
Page 756 and 757: Subject Index 741 Full rational gro
Page 758 and 759: Subject Index 743 Łoś-Eda theorem
Page 760 and 761: Subject Index 745 Rank 1 torsion-fr
Page 762: Subject Index 747 vector space, 334
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Abelian Groups - László Fuchs [Springer]

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