Author: Evgenii I. Khukhro
Publisher: Cambridge University Press
ISBN: 052159717X
Category : Mathematics
Languages : en
Pages : 226

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Book Description
Ideal for graduate students and researchers working in group theory and Lie rings.

Author: M. Aschbacher
Publisher: Cambridge University Press
ISBN: 9780521786751
Category : Mathematics
Languages : en
Pages : 320

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Book Description
During the last 40 years the theory of finite groups has developed dramatically. The finite simple groups have been classified and are becoming better understood. Tools exist to reduce many questions about arbitrary finite groups to similar questions about simple groups. Since the classification there have been numerous applications of this theory in other branches of mathematics. Finite Group Theory develops the foundations of the theory of finite groups. It can serve as a text for a course on finite groups for students already exposed to a first course in algebra. It could supply the background necessary to begin reading journal articles in the field. For specialists it also provides a reference on the foundations of the subject. This second edition has been considerably improved with a completely rewritten Chapter 15 considering the 2-Signalizer Functor Theorem, and the addition of an appendix containing solutions to exercises.

Author: Inder Bir Singh Passi
Publisher: Springer
ISBN: 9811328951
Category : Mathematics
Languages : en
Pages : 231

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Book 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.

Author: J. D. Dixon
Publisher: Cambridge University Press
ISBN: 9780521542180
Category : Mathematics
Languages : en
Pages : 392

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Book Description
An up-to-date treatment of analytic pro-p groups for graduate students and researchers.

Author: Mima Stanojkovski
Publisher: American Mathematical Society
ISBN: 1470450038
Category : Mathematics
Languages : en
Pages : 117

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Book Description
View the abstract.

Author: Yakov G. Berkovich
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110533146
Category : Mathematics
Languages : en
Pages : 410

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Book Description
This is the sixth volume of a comprehensive and elementary treatment of finite group theory. This volume contains many hundreds of original exercises (including solutions for the more difficult ones) and an extended list of about 1000 open problems. The current book is based on Volumes 1–5 and it is suitable for researchers and graduate students working in group theory.

Author: Daniel Gorenstein
Publisher: American Mathematical Soc.
ISBN: 9780821803905
Category : Mathematics
Languages : en
Pages : 246

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Book Description
The second volume of a series devoted to reorganizing and simplifying proof of the classification of the finite simple groups. In a single chapter, it lays the groundwork for the forthcoming analysis of finite simple groups, beginning with the theory of components, layers, and the generalized Fitting subgroup, which has been developed largely since Gorenstein's basic 1968 text and is now central to understanding the structure of finite groups. Suitable as an auxiliary text for a graduate course in group theory. Member prices are $35 for individual and $47 for institutions. Annotation copyright by Book News, Inc., Portland, OR

Author: Yakov G. Berkovich
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110295350
Category : Mathematics
Languages : en
Pages : 434

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Book Description
This is the fifth volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume include theory of linear algebras and Lie algebras. The book contains many dozens of original exercises (with difficult exercises being solved) and a list of about 900 research problems and themes.

Author: Clive Mortimer Reis
Publisher:
ISBN:
Category : Finite groups
Languages : en
Pages : 110

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Book Description

Author: Yakov Berkovich
Publisher: Walter de Gruyter
ISBN: 3110208237
Category : Mathematics
Languages : en
Pages : 613

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Book Description
This is the second of three volumes devoted to elementary finite p-group theory. Similar to the first volume, hundreds of important results are analyzed and, in many cases, simplified. Important topics presented in this monograph include: (a) classification of p-groups all of whose cyclic subgroups of composite orders are normal, (b) classification of 2-groups with exactly three involutions, (c) two proofs of Ward's theorem on quaternion-free groups, (d) 2-groups with small centralizers of an involution, (e) classification of 2-groups with exactly four cyclic subgroups of order 2n > 2, (f) two new proofs of Blackburn's theorem on minimal nonmetacyclic groups, (g) classification of p-groups all of whose subgroups of index p2 are abelian, (h) classification of 2-groups all of whose minimal nonabelian subgroups have order 8, (i) p-groups with cyclic subgroups of index p2 are classified. This volume contains hundreds of original exercises (with all difficult exercises being solved) and an extended list of about 700 open problems. The book is based on Volume 1, and it is suitable for researchers and graduate students of mathematics with a modest background on algebra.