Automorphisms of finite groups
Material type:
TextLanguage: English Series: Springer Monographs in MathematicsPublication details: Singapore : Springer Nature, 2018. Description: xix, 217pISBN: 9789811328947Subject(s): Functions of complex variables | Group theory | Lie groups | Number theory | Topological groups | Automorphisms | Divisibility Property | Coclass tree | Central automorphism | Group cohomology | Schur multiplier | Uniform Lie algebraDDC classification: 512.542.2 Online resources: Table of Content | Reviews Summary: The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.
| Item type | Current library | Call number | Status | Date due | Barcode |
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Book
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SMS Library | 512.542.2 PAS-A (Browse shelf(Opens below)) | Available | 25189 |
Includes bibliographical references and index.
The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.
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