Ischia Group Theory 2008 : Proceedings of the Conference in Group Theory.
Title:
Ischia Group Theory 2008 : Proceedings of the Conference in Group Theory.
Author:
Bianchi, Mariagrazia.
ISBN:
9789814277808
Personal Author:
Physical Description:
1 online resource (315 pages)
Contents:
Contents -- Preface -- Sponsors -- Conference Program -- Registered Participants -- On Abnormal Maximal Subgroups of Finite Groups A. Ballester-Bolinches, J. Cossey and R. Esteban-Romero -- 1. Introduction -- Acknowledgments -- References -- Finite Gelfand Pairs: Examples and Applications T. Ceccherini-Silberstein, D. D'Angeli, A. Donno, F. Scarabotti and F. Tolli -- 1. Introduction -- 2. Finite Gelfand pairs -- 2.1. Definitions -- 2.2. First examples -- 2.3. Characterizations of finite Gelfand pairs -- 2.4. Spherical functions -- 2.5. The spherical Fourier transform -- 2.6. Applications of the spherical Fourier transform to probability -- 2.7. An example and an application: the Johnson scheme and the Bernoulli-Laplace diffusion model -- 2.8. Other fundamental examples -- 3. Trees, wreath products and nite Gelfand pairs -- 3.1. The Gelfand pair (Aut(Tr) -- K(r -- s)) -- 3.2. Composition and exponentiation of Gelfand pairs -- 3.3. The generalized Johnson scheme -- 3.4. The end of the story -- 4. Groups acting on trees. -- 5. Gelfand pairs and self-similar groups -- 6. Gelfand pairs and generalized wreath products of permutation groups -- 6.1. Preliminaries -- 6.2. The generalized wreath product -- 6.3. Gelfand pairs -- 6.4. Spherical functions -- Acknowledgments -- References -- On Blichfeldt's Like Congruences and Other Close Characters
2. Finite XT-groups -- 3. Infinite XT-groups -- 4. Infinite polycyclic-transitive groups -- References -- Some Simple Locally (Soluble-by-Finite) Groups M.R. Dixon, M.J. Evans and H. Smith -- 1. Introduction -- 2. Embedding groups in simple groups -- 3. Some constructions for simple locally (soluble-by- nite) groups -- Acknowledgements -- References -- The Fundamental Group of a Connected Undirected Pro nite Graph W. Herfort -- Introduction -- 1. Profinite graphs -- 1.1. Definition of ( ) -- 1.2. Orientable pro nite graphs -- 1.3. Products, equalizers and projective limits -- 2. Graph actions and G-graphs -- 2.1. General definitions -- 3. Galois covers -- 3.1. A non-orientable simply connected graph -- 3.2. Description of the fundamental group of a connected graph -- Acknowledgements -- References -- On a Graph Associated with a Group D. Imperatore -- 1. Introduction -- 2. Some examples and properties -- 3. The abelian case -- 4. The nilpotent case -- 5. The supersolvable case -- Bibliography -- Some Exceptional Minimal Situations by Finite p-groups Z. Janko -- References -- Regular Limits of In nite Symmetric Groups O. H. Kegel -- 1. Introduction -- 2. Bounded Subgroups of S for a limit ordinal -- 3. Belyaev factorised groups -- 4. Existentially closed groups -- 5. Universal Groups -- References -- Large Normal and Characteristic Subgroups Satisfying Outer Commutator Identities and their Applications E.I. Khukhro -- Introduction -- 1. Subgroups of finite index -- 2. Ideals of bounded codimension -- 3. Subgroups of bounded co-rank -- 4. Generalizations -- 5. Families of normal subgroups and ideals satisfying an outer commutator law -- 6. Applications -- References -- Soluble Linear Groups with Some Restrictions on Subgroups of In nite Central Dimension L.A. Kurdachenko, J.M. Mu~noz-Escolano and J. Otal -- 1. Introduction.
2. Soluble groups satisfying Wmin{icd or Wmax-icd -- 3. The finitarity of soluble linear groups with Wmin-icd of positive characteristic -- 4. The finitarity of soluble linear groups with Wmin{icd of characteristic zero -- Acknowledgments -- References -- Character Tables of Groups Where All Nonlinear Irreducible Characters Vanish O the Center M.L. Lewis -- References -- Some Results and Questions Related to the Generating Graph of a Finite Group A. Lucchini and A. Mar oti -- 1. Introduction -- 2. Covering groups with proper subgroups -- 3. The non-commuting graph -- 4. The generating graph -- 5. Solvable groups -- 6. Artinian rings -- 7. Arc transitive graphs -- 8. A probabilistic method -- 9. Systems of distinct representatives -- 10. Affine groups -- References -- On the Minimal Irreucibility of the Unipotent Characters of the Finite Unitary Groups M.A. Pellegrini -- 1. Introduction -- 2. Tools -- 2.1. Restricting characters to subgroups belonging to the Aschbacher class C -- 2.2. Zsigmondy primes -- 3. The odd dimensional `generic' case -- 4. The even dimensional `generic' case -- 5. The low-dimensional cases -- 5.1. G = PSU(2 -- q) -- 5.2. G = PSU(3 -- q) -- 5.3. G = PSU(4 -- q) -- 5.4. G = PSU(5 -- q) -- 5.5. G = PSU(6 -- q) -- References -- A Note on Relative Isoclinism Classes of Compact Groups R. Rezaei and F. Russo -- 1. Some Recent Results -- 2. Improvements -- References -- Restrictions of Brauer Characters and -partial Characters J. Sangroniz -- 1. Introduction -- 2. Restriction of Brauer characters -- 3. Restriction of -partial characters -- Acknowledgments -- References -- Real Characters and Degrees: An Overview L. Sanus -- 1. Introduction -- 2. Results -- References -- Varieties of Groups and the Restricted Burnside Problem P. Shumyatsky and J.C. Silva -- 1. Introduction.
2. The Restricted Burnside Problem for Multilinear Commutators -- 3. The Restricted Burnside Problem for Engel Words -- 4. Some Proofs -- Deduction of Theorem 4.1 from Proposition 4.6 -- References -- The (2 -- 3)-generation of Matrix Groups Over the Integers M.C. Tamburini -- 1. Introduction -- 2. Definition of the generators -- 3. The action of their commutator -- 4. The group generated by x and y -- References -- p-Projective Groups and Pro-p Trees T. Weigel -- 1. Introduction -- 2. p-Projective pro nite groups -- 2.1. Homomorphic images of p-projective profinite groups -- 2.2. p-Frattini extensions -- 2.3. p-Projective covers -- 3. Profinite graphs -- 3.1. Boolean spaces -- 3.2. Profinite graphs -- 3.3. Profinite G-sets -- 3.4. Profinite groups acting on profinite graphs -- 3.5. Abelian pro-p groups -- 3.6. The characteristic Zp-complex associated to a pro nite graph -- 4. Profinite Z [[G]]-modules -- 4.1. Projective pro nite Zp[[G]]-modules -- 4.2. The completed tensor product -- 4.3. Induction and deflation -- 4.4. Profinite G-sets and Zp[[G]]-modules -- 4.5. Profinite groups acting on pro-p trees -- 4.6. Good groups of type FP -- 5. Finite graphs of finite groups and their fundamental groups -- 5.1. Finite graphs of finite groups -- 5.2. Free Zp-modules -- 5.3. The universal p-projective p-cover of a finite p-perfect group -- 5.4. Theorem C -- 6. The p-Lefschetz number for virtual pro-p groups of type p-FP -- 6.1. Traces -- 6.2. Hattori-Stallings ranks for projective modules of finite groups -- 6.3. Deflation -- 6.4. Virtual pro-p groups -- 6.5. The p-Lefschetz number for virtual pro-p group of type p-FP -- 6.6. The p-Lefschetz number of the universal p-Frattini covers of a finite group -- References.
Abstract:
The volume contains a collection of research articles by leading experts in group theory, and reports of several accessible surveys of recent research in the area. The compilation provide an overview of the diversity of themes and applications that interest today's group theorists. The topics covered in this volume include: character theory, combinatorial group theory, varieties of groups, conjugacy classes, profinite groups, graphs connected with groups, subgroup structure, representation theory. Sample Chapter(s). Chapter 1: On abnormal maximal subgroups of finite groups (107 KB). Contents: On Abnormal Maximal Subgroups of Finite Groups (A Ballester-Bolinches et al.); Finite Gelfand Pairs: Examples and Applications (T Ceccherini-Silberstein et al.); On Blichfeld's Like Congruences and Other Close Characters - Conjugacy Classes Analogs (D Chillag); Permutation Groups Defined by Unordered Relations (F Dalla Volta & J Siemons); Transitivity of Properties of 2-Generator Subgroups (C Delizia et al.); Some Simple Locally (Soluble-by-Finite) Groups (M R Dixon et al.); The Fundamental Group of a Connected Undirected Profinite Graph (W Herfort); On a Graph Associated with a Group (D Imperatore); Some Exceptional Minimal Situations by Finite p -Groups (Z Janko); Regular Limits of Infinite Symmetric Groups (O H Kegel); Large Normal and Characteristic Subgroups Satisfying Outer Commutator Identities and Their Applications (E I Khukhro); Soluble Linear Groups with Some Restrictions on Subgroups of Infinite Central Dimension (L A Kurdachenko et al.); Character Tables of Groups Where All Nonlinear Irreducible Characters Vanish Off the Center (M L Lewis); Some Results and Questions Related to the Generating Graph of a Finite Group (A Lucchini & A Maróti); On the Minimal Irreucibility of the Unipotent Characters of the Finite Unitary Groups (M A Pellegrini); A
Note on Relative Isoclinism Classes of Compact Groups (R Resaei & F Russo); Restrictions of Brauer Characters and π-Partial Characters (J Sangroniz); Real Characters and Degrees: An Overview (L Sanus); Varieties of Groups and the Restricted Burnside Problem (P Shumyatsky & J C Silva); The (2,3)-Generation of Matrix Groups Over the Integers (M C Tamburini); p -Projective Groups and Pro- p Trees (T Weigel);. Readership: Researchers in group theory.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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