Automorphisms of Finite Groups / by Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav.

Format:

Book

Author/Creator:

Passi, Inder Bir Singh, author.

Singh, Mahender, author.

Yadav, Manoj Kumar, author.

Contributor:

SpringerLink (Online service)

Series:

Mathematics and Statistics (Springer-11649)

Springer monographs in mathematics 1439-7382

Springer Monographs in Mathematics, 1439-7382

Language:

English

Subjects (All):

Group theory.

Topological groups.

Lie groups.

Functions of complex variables.

Number theory.

Group Theory and Generalizations.

Topological Groups, Lie Groups.

Several Complex Variables and Analytic Spaces.

Number Theory.

Local Subjects:

Group Theory and Generalizations.

Topological Groups, Lie Groups.

Several Complex Variables and Analytic Spaces.

Number Theory.

Physical Description:

1 online resource (XIX, 217 pages) : 1 illustrations.

Edition:

First edition 2018.

Contained In:

Springer eBooks

Place of Publication:

Singapore : Springer Singapore : Imprint: Springer, 2018.

System Details:

text file PDF

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.

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.

Other Format:

Printed edition:

ISBN:

978-981-13-2895-4

9789811328954

Access Restriction:

Restricted for use by site license.