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" Automorphisms of finite groups / "
Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav.
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BL
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| Record Number
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891506
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| Main Entry
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Passi, Inder Bir S.,1939-
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| Title & Author
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Automorphisms of finite groups /\ Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav.
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| Publication Statement
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Singapore :: Springer,, 2018.
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| Series Statement
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Springer monographs in mathematics,
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| Page. NO
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1 online resource
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| ISBN
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9789811328954
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: 9789811328961
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: 9811328951
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: 981132896X
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9789811328947
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9811328943
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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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
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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
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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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| Abstract
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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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| Subject
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Automorphisms.
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Finite groups.
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Automorphisms.
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Finite groups.
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MATHEMATICS-- Algebra-- Intermediate.
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| Dewey Classification
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512/.23
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| LC Classification
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QA171
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| Added Entry
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Singh, Mahender
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Yadav, Manoj Kumar
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