Abstract Algebra Theory and Applications - Computer Science ...

420 INDEXnormalizer of, 222proper, 46stabilizer, 205Sylow p-subgroup, 222torsion, 70transitive, 88translation, 183trivial, 46Subnormal series of a group, 195Subring, 236Supremum, 296Switchclosed, 305definition of, 305open, 305Switching function, 214, 311Sylow p-subgroup, 222Sylow, Ludvig, 224Syndrome of a code, 128, 363Weight of a codeword, 114Weil, André, 342Well-defined map, 10Well-ordered set, 25Whitehead, Alfred North, 308Wilson’s Theorem, 362Zassenhaus Lemma, 200Zeromultiplicity of, 368of a polynomial, 262Zero divisor, 234Tartaglia, 270Third Isomorphism Theoremfor groups, 165for rings, 243Thompson, J., 161, 217Totally ordered set, 310Transcendental element, 325Transcendental number, 325Transposition, 77Trisection of an angle, 341Unique factorization domain (UFD), 282Unit, 233, 282Universal Product Code, 53Upper bound, 296Vandermonde determinant, 356Vandermonde matrix, 356Vector spacebasis of, 317definition of, 312dimension of, 317direct sum of, 320dual of, 320subspace of, 314