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Automorphisms of finite groups

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Automorphisms of finite groups/ by Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav.
Author:	Passi, Inder Bir Singh.
other author:	Singh, Mahender.
Published:	Singapore :Springer Singapore : : 2018.,
Description:	xix, 217 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Finite groups. -
Online resource:	https://doi.org/10.1007/978-981-13-2895-4
ISBN:	9789811328954

Automorphisms of finite groups
Passi, Inder Bir Singh.

Automorphisms of finite groups[electronic resource] /by Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav. - Singapore :Springer Singapore :2018. - xix, 217 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

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.

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.

ISBN: 9789811328954

Standard No.: 10.1007/978-981-13-2895-4doiSubjects--Topical Terms:

684448
Finite groups.

LC Class. No.: QA171 / .P377 2018

Dewey Class. No.: 512.23

Automorphisms of finite groups
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100 1 $a Passi, Inder Bir Singh. $3 896078
245 1 0 $a Automorphisms of finite groups $h [electronic resource] / $c by Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav.
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300 $a xix, 217 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 1439-7382
505 0 $a 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.
520 $a 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.
650 0 $a Finite groups. $3 684448
650 0 $a Automorphisms. $3 905109
650 1 4 $a Group Theory and Generalizations. $3 672112
650 2 4 $a Topological Groups, Lie Groups. $3 672074
650 2 4 $a Several Complex Variables and Analytic Spaces. $3 672032
650 2 4 $a Number Theory. $3 672023
700 1 $a Singh, Mahender. $3 1211813
700 1 $a Yadav, Manoj Kumar. $3 1209606
710 2 $a SpringerLink (Online service) $3 593884
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950 $a Mathematics and Statistics (Springer-11649)