CURRICULUM VITAE Orazio Puglisi Date and place of birth : july 17 ...

CURRICULUM VITAE
Orazio Puglisi
Date and place of birth : july 17 1962, Vieste (Foggia).
Nationality: Italian
Address: Dipartimento di Matematica ”U. Dini”, Università di Firenze, viale Morgagni
67/A, 50134 Firenze (Italy)
Academic career
Laurea in Matematica, University of Padova, November10 1986.
PhD in Mathematics, University of Florence, july 9 1993
1990-2000 Assistant professor, Faculty of Science, University of Trento.
August 1991-February 1992. Visisting Scholar, Michigan State University.
April 2000 LMS grant.
September 2000 Associate professor, Faculty of Science, University of Florence.
June 2000 LMS grant.
Augusr 2004 Visiting professor, National University of Ireland, Galway, Ireland.
.
a.y. 1990-91. Exercise classes in Algebra.
Teaching
a.y. 1991-92. Exercise classes in Algebra and exercise class in Linear Algebra..
a.y. 1992-93. Exercise classes in Algebra.
a.y. 1993-94. Exercise classes in Algebra.
a.y. 1993-94. Linear groups (PhD course)
a.y. 1994-95. Exercise classes in Algebra.
a.y. 1994-95. Advanced Algebra.
a.y. 1995-96. Algebra.
a.y. 1996-97. Exercise classes in Algebra.
a.y. 1996-97. Exercise classes in Linear Algebra.
a.y. 1997-98. Exercise classes in Linear Algebra.
a.y. 1997-98. Number Theory
a.y. 1998-99. Exercise classes in Linear Algebra and exercise classes in Discrete Mathematics.
a.y. 2000-01. Group theory.
a.y. 2000-01. Criptography.
a.y. 2001-02. Algebra.
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a.y. 2001-02. Criptography.
a.y. 2001-02. Algebraic number theory (PhD course).
a.y. 2002-03. Algebra.
a.y. 2002-03. Criptography.
a.y. 2003-04. Algebra.
a.y. 2003-04. Criptography.
a.y. 2004-05. Algebra.
a.y. 2004-05. Criptography.
a.y. 2004-05. Number Theory
a.y. 2005-06. Algebra.
a.y. 2005-06. Criptography.
a.y. 2005-06. Number Theory
a.y. 2006-07. Algebra.
a.y. 2006-07. Criptography.
a.y. 2006-07. Number Theory
Schools and Meetings
Here below is a list of schools and meetings The title of the talk given (if any) is given
in brackets.
july 1986. Summer school SMI in Perugia. Attended courses: Complex Analysis (prof. B.
Aupetit) and Group Theory (prof. E. Robertson)
july 1988. Summer school SMI in Perugia. Attended courses: Functional Analysis (prof.
Volcic) and Algebra (prof. Valla).
june 1989. International Conference in Group Theory, Brixen/Bressanone.
june 1990. Gruppen und topologische Gruppen, Trento.
september 1990. Representation theory II, Trento.
july 1990. Summer school SMI in Cortona “Automorphisms groups” (prof. F. Menegazzo)
and ”Finitary groups” ( prof. R. Phillips).
february 1991. Order in Algebra and Logic, Napoli.
june 1991. School in Non-commutative algebra Parma.
june 1991. Gruppen und topologische Gruppen, München (Locally solvable groups).
june 1992. Gruppen und topologische Gruppen, Erlangen.
april 1993. Group Theory (Characters and structure), Trento.
june 1993. Gruppen und topologische Gruppen, Trento.
august 1993 International conference on Group Theory, Galway (Ireland).
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may 1994. Infinite Groups, Ravello.
august 1994. NATO Advanced Study Institute , Finite and Locally Finite Groups, Istanbul.
september 1994. “Generators and relations in group theory”, Cortona.
september 1995 Linear groups, Levico (Maximal unipotent subgroups of finitary linear
groups).
february 2003 “Advanced course on contemporay cryptography” CRM Barcelona.
june 2003 Meeting on ”Group Theory” Brixen.
september 2007 Meeting ”Profinite and asymptotic group theory” Levico
Invitations to meetings
Here it follows a list of meetings which I attended as invited speaker. The title of the
talk given is indicated in brackets.
january 1994. Permutation groups, Oberwolfach (Germany) (Automorphisms groups
of hypercentral p-groups).
may 1996. Workshop RiP on “Simple Locally finite groups” Oberwolfach (Isomorphism
and conjugacy of Sylow subgroups of finitary groups).
july 1996. European Research Conference “Group Theory: Finite to Infinite”, il
Ciocco (Which groups are finitary linear?).
may 1998 Finite and locally finite groups with applications, Levico (Irreducible finitary
Lie algebras I).
october 1998 Due giornate in onore di Mario Curzio, Napoli (Images and representations
of finitary groups).
january 2000 Workshop “Teoria dei gruppi e applicazioni”, Milano ( Sottogruppi confinati
nei gruppi semplici).
may 2001 Conference “Groups in Galway”, Galway (IR) (Group algebras of locally
finite simple groups).
Invited Talks
This is a list of talks given in various universities.
october 1990. Michigan State University: “Outer automorphisms of locally finite pgroups”.
december 1990. Michigan State University:“ A topology for finitary linear groups”.
july 1993. University of Napoli:“Tit’s alternativev for finitary groups”.
december 1993. University of Padova: “Automorphisms of infinite p-groups”.
may 1996. University of Mainz: “Sylow subgroups of finitary linear groups”.
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may 1997 University of Padova “Sylow subgroups of finitary linear groups”.
april 1998 University of Padova “Finitary Lie algebras ”
june 1998. University of Mainz: “Automorphisms of nilpotent and related groups”.
november 1998. University of Brescia “ Recognizing finitary groups”.
march 1999. University of Florence “ Simple locally finite groups”.
december 1999 University of Ljubljana “Linear groups and their generalizations”.
april 2000 University of Newcastle “Confined subgroups in locally finite simple groups”.
november 2002 Università di Firenze, Mathesis colloquium, “ Crittografia”.
june 2003 Università di Verona, “Alcuni attacchi ad RSA”.
october 2004 Università di Firenze, Mathesis colloquium, ”Short course in Criptography”.
Organization of Meetings
July 1999 Workshop ”Model Theory and Permutation Groups” (Trento), jointly with Stefano
Baratella.
September 2000 School ”Finiteness Conditions in Group Theory” (Cotronei), jointly
with Brunella Bruno and Francesco de Giovanni.
Publications
1. On outer automorphisms of Cernikov p-groups, Rend. Sem. Mat. Univ. Padova
83 (1990), 97-106.
In this paper a celebrated theorem by Gaschütz on the existence of outer p-automorphisms
of finite p-groups, is extended to a class of Cernikov groups.
2. (with R. Phillips e U. Meierfrankenfeld) Locally solvable finitary linear groups,
Journal of the London Mathematical Society (2) 47 (1993) 31-40.
In this paper we describe the structure of locally solvable finitary groups, proving an analog
of the Malcev’s structure theorem of solvable linear groups.
3. A note on the automorphism group of a locally finite p-group, Bullettin of the
London mathematical Society 24 (1992) 437-441.
Here it is proved that a locally finite countable p-group, always has uncountable automorphisms
group.
4. (with F. Leinen) Unipotent finitary linear groups, Journal of the London Mathematical
Society (2) 48 (1993) 59-76.
A number of questions concerning existentially closed groups in finitary classes is studied.
In particular the existentially closed objects are described.
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5. Homomorphic images of finitary linear groups, Arch. Math. Basel 60 (1993)
497-504.
In this paper the ”Tit’s” alternative is proved for finitary linear groups. Moreover homomorphic
images of finitary linear groups are studied, showing that, for such groups, many
features of finitary groups are still valid.
6. (with L. S. Spiezia ) A combinatorial property of certain infinite groups, Communications
in Algebra 22 (4) 1457-1465 (1994).
Here we study a generalization of a problem raised by Erdos.
7. Outer automorphisms of hypercentral p-groups, Glasgow Math. Journal 37 (1995)
243-247.
Hypercentral p-groups aer studied in order to decide if an analog of Gaschütz theorem
holds. It is proved that this is the case when the hypercentral height is ω.
8. (with A. Lucchini) A note on groups satisfying the congruence intersection property,
Proceedings of the Royal Irish Academy 97A n.1 (1997) 61-68.
Here we study a property arising from universal algebra. We classify groups in which this
property holds, showing that, in most cases, they are Dedekind groups.
9. Free products of finitary linear groups, Proceedings of the A.M.S. 124 n. 4 (1996)
1027-1033
The main result is that a free product of finitary groups is again finitary. This fact is
used to show that free groups of arbitrary infinite rank are finitary over fields of arbitrary
characteristic.
10. Maximal unipotent subgroups of finitary linear groups, J. Algebra 181 (1996)
628-658.
In this paper a complete description of the maximal unipotent subgroups of FGL(V, F ) is
given. Their equivalence is also described.
11. Sylow subgroups of finitary linear groups, Geometriae Dedicata 63 (1996) 95-112.
Here the structure and equivalence of Sylow subgroups of FGL(V, F ) is determined.
12. (with F.Leinen) Countably recognizability of primitive periodic finitary linear
groups, Math. Proc. Camb. Phil. Soc. 121 (1997) 425-435
In this paper we show that locally finite primitive finitary groups are countably recognizable.
13. (with F.Leinen) Periodic groups covered by transitive subgroups of finitary permutations
or by irreducible subgroups of finitary transformations, Transactions of the
A.M.S. 352 n.4 (2000) 1913-1934
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The problem of countable recognizability is investigated for imprimitivite finitary groups.
Contrary to the primitive case, only p-groups in this class are countably recognizable.
Some explicit counterexamples are constructed.
14. (with L. S. Spiezia ) Groups with all subgroups graph complete, Alg. Colloquium.
5: 4 (1998) 377-382
Given a finite group G, there is a graph associated to it, whose vertices are the non-trivial
conjugacy classes. In this paper we show that, if this graph is complete for every subgroup
of G, then G is solvable.
15. (with F.Leinen) Serial subalgebras of finitary Lie algebras, Proceedings of the
A.M.S. 129 n.1 (2000) 45–51
In this paper we prove that, in an irreducible finitary Lie algebras, no locally solvable
ascendant subalgebras are present, unless the algebra is finite dimensional. As a by-product
we obtain a structure theorem for finitary locally solvable Lie algebras.
16. (with F.Leinen) Irreducible finitary Lie algebras over fields of characteristic zero,
J. Algebra 210 (1998) 697-702.
Here we prove that, if L is an irreducible finitary Lie algebra of infinite dimension, then
L ′ is simple, unless L is finite dimensional.
17. (with F.Leinen) Irreducible finitary Lie algebras over fields of positive characteristic
, Math. Proc. Cambridge Philos. Soc. 129 (2000), no. 1, 1–8.
Here we prove that, if L is an irreducible finitary Lie algebra of infinite dimension, then
L (5) is simple, unless L is finite dimensional.
18 (with F. Menegazzo) Outer automorphisms of supersoluble groups, Glasgow Math.
Jour. 42 (2000) 115-120.
The existence of non-inner automorphisms for torsion-free supersolvable groups has been
an open problem for a long time. Here we prove that, if G/G ′ is finite, then G may have
only inner automorphisms.
19 (with F.Leinen ) Finitary representations and images of transitive finitary permutation
groups, J. Algebra 222 (1999) 524-549.
In this paper we study quotients of transistive groups of finitary permutations, giving
condition under which this still have a finitary faithful representation. In doing that we
find the number of inequivalent finitary representations.
20 (with F. Leinen) Confined subgroups in periodic simple finitary linear groups,
Israel Journal of Mathematics 128 (2002) 285–324.
In this paper we determine the confined subgroups of locally finite simple groups which
are finitary.
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21 (with F. Leinen) Ideals in group algebras of simple locally finite groups of 1-type,
Pacific Journal of Mathematics, 207 n.2 (2002) 433–446.
In this paper we study the ideal structure of group algebras of simple locally finite groups
of 1-type.
22 (with F. Leinen) Diagonal limits of finite alternating groups. Confined subgroups,
ideals, and positive definite functions, Illinois Journal of Mathematics 47 n.1/2 (2003)
345–360. .
In this paper confined subgroups of diagonal limits of alternating groups are described.
Moreover their relations with ideals of the group algebras and with positive definite functions
of CG are determined.
23( with F. Leinen) Positive definite functions on diagonal limits of finite alternating
groups, groups. J. London Math. Soc. (2) 70 (2004), no. 3, 678–690.
24 (with F. Leinen) Some remarks on groups of 1-type, J. Algebra 287 (2005), no. 1,
32–51.
25 (with F. Leinen) Positive definite functions of finitary isometry groups over fields
of odd characteristic, J. Pure Appl. Algebra 208 (2007), no. 3, 1003–1021.
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