Automorphisms of finite groups
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Bibliographic Information
Automorphisms of finite groups
Springer, c2018 , [Printforce]
- : [hardcover]
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Description based on: [hardcover], c2018
[Reprint]. Originally published: Singapore : Springer , c2018
"Printed by Printforce, the Netherlands"--P. [226]
"(C) Springer Nature Singapore Pte Ltd. 2018"--T.p.verso
Originally issued in the series: Springer monographs in mathematics
Includes bibliographical references (p. 209-213) and index
Description and Table of Contents
Description
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.
Table of Contents
Introduction.- p-groups.- Fundamental exact sequence of Wells.- Automorphism groups of finite groups.- Groups with Divisibility Property-I.- Groups with Divisibility Property-II.- Groups without Divisibility Property.
by "Nielsen BookData"
