Automorphisms of finite groups /

Automorphisms of finite groups /

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Bibliographic Details
Author / Creator:Passi, Inder Bir S., 1939- author.
Imprint:Singapore : Springer, 2018.
Description:1 online resource
Language:English
Series:Springer monographs in mathematics, 1439-7382
Springer monographs in mathematics.
Subject:
Finite groups.
Automorphisms.
Automorphisms.
Finite groups.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11781020
Hidden Bibliographic Details
Other authors / contributors:Singh, Mahender, author.
Yadav, Manoj Kumar, author.
ISBN:9789811328954
9811328951
9789811328947
9811328943
9789811328961
981132896X
Digital file characteristics:text file PDF
Notes:Includes bibliographical references and index.
Online resource; title from PDF title page (SpringerLink, viewed January 21, 2019).
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.--
Other form:Print version: Passi, Inder Bir S., 1939- Automorphisms of finite groups. Singapore : Springer, 2018 9811328943 9789811328947
Standard no.:10.1007/978-981-13-2895-4
Table of Contents:
  • Intro; Preface; Acknowledgements; Contents; About the Authors; Notation; 1 Preliminaries on p-Groups; 1.1 Central Series; 1.2 Regular Groups; 1.3 Groups with Large Center; 1.4 Gaschütz's Theorem and Its Generalization; 1.5 Pro-p-Groups; 2 Fundamental Exact Sequence of Wells; 2.1 Cohomology of Groups; 2.2 Group Extensions; 2.3 Action of Cohomology Group on Extensions; 2.4 Action of Automorphism Group on Extensions; 2.5 Action of Automorphism Group on Cohomology; 2.6 Wells Map; 2.7 Wells Exact Sequence; 2.8 Extensions with Trivial Coupling; 2.9 Extension and Lifting of Automorphisms
  • 3 Orders of Automorphism Groups of Finite Groups3.1 Schur Multiplier; 3.2 Automorphisms of Finite Abelian Groups; 3.3 Ledermann-Neumann's Theorem; 3.4 Green's Function; 3.5 Howarth's Function; 3.6 Hyde's Function; 4 Groups with Divisibility Property-I; 4.1 Reduction Results; 4.2 Groups of Nilpotency Class 2; 4.3 Groups with Metacyclic Central Quotient; 4.4 Modular Groups; 4.5 p-Abelian Groups; 4.6 Groups with Small Central Quotient; 5 Groups with Divisibility Property-II; 5.1 Groups of Order p7; 5.2 Groups of Coclass 2; 5.3 2-Groups of Fixed Coclass; 5.4 p2-Abelian p-Central Groups
  • 5.5 Further Results6 Groups Without Divisibility Property; 6.1 Lie Algebras and Uniform Pro-p-Groups; 6.2 Existence of Groups Without Divisibility Property; References; Index

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