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Groups of Prime Power Order. Volume 5

Groups of Prime Power Order. Volume 5
Author: Yakov G. Berkovich
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 434
Release: 2016-01-15
Genre: Mathematics
ISBN: 3110295350

Download Groups of Prime Power Order. Volume 5 Book in PDF, ePub and Kindle

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.


Groups of Prime Power Order

Groups of Prime Power Order
Author: Yakov G. Berkovich
Publisher:
Total Pages: 411
Release: 2016
Genre:
ISBN: 9783110295344

Download Groups of Prime Power Order Book in PDF, ePub and Kindle

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.


Groups of Prime Power Order. Volume 6

Groups of Prime Power Order. Volume 6
Author: Yakov G. Berkovich
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 495
Release: 2018-06-25
Genre: Mathematics
ISBN: 3110531003

Download Groups of Prime Power Order. Volume 6 Book in PDF, ePub and Kindle

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.


Groups of Prime Power Order. Volume 1

Groups of Prime Power Order. Volume 1
Author: Yakov Berkovich
Publisher: Walter de Gruyter
Total Pages: 533
Release: 2008-12-10
Genre: Mathematics
ISBN: 3110208229

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This is the first of three volumes of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this monograph include: (a) counting of subgroups, with almost all main counting theorems being proved, (b) regular p-groups and regularity criteria, (c) p-groups of maximal class and their numerous characterizations, (d) characters of p-groups, (e) p-groups with large Schur multiplier and commutator subgroups, (f) (p‒1)-admissible Hall chains in normal subgroups, (g) powerful p-groups, (h) automorphisms of p-groups, (i) p-groups all of whose nonnormal subgroups are cyclic, (j) Alperin's problem on abelian subgroups of small index. The book is suitable for researchers and graduate students of mathematics with a modest background on algebra. It also contains hundreds of original exercises (with difficult exercises being solved) and a comprehensive list of about 700 open problems.


Groups of Prime Power Order. Volume 3

Groups of Prime Power Order. Volume 3
Author: Yakov Berkovich
Publisher: Walter de Gruyter
Total Pages: 669
Release: 2011-06-30
Genre: Mathematics
ISBN: 3110254484

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This is the third volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume: impact of minimal nonabelian subgroups on the structure of p-groups, classification of groups all of whose nonnormal subgroups have the same order, degrees of irreducible characters of p-groups associated with finite algebras, groups covered by few proper subgroups, p-groups of element breadth 2 and subgroup breadth 1, exact number of subgroups of given order in a metacyclic p-group, soft subgroups, p-groups with a maximal elementary abelian subgroup of order p2, p-groups generated by certain minimal nonabelian subgroups, p-groups in which certain nonabelian subgroups are 2-generator. The book contains many dozens of original exercises (with difficult exercises being solved) and a list of about 900 research problems and themes.


Groups of Prime Power Order. Volume 4

Groups of Prime Power Order. Volume 4
Author: Yakov G. Berkovich
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 476
Release: 2015-12-14
Genre: Mathematics
ISBN: 3110281473

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This is the fourth volume of a comprehensive and elementary treatment of finite p-group theory. As in the previous volumes, minimal nonabelian p-groups play an important role. Topics covered in this volume include: subgroup structure of metacyclic p-groups Ishikawa’s theorem on p-groups with two sizes of conjugate classes p-central p-groups theorem of Kegel on nilpotence of H p-groups partitions of p-groups characterizations of Dedekindian groups norm of p-groups p-groups with 2-uniserial subgroups of small order The book also contains hundreds of original exercises and solutions and a comprehensive list of more than 500 open problems. This work is suitable for researchers and graduate students with a modest background in algebra.


Identical Relations in Lie Algebras

Identical Relations in Lie Algebras
Author: Yuri Bahturin
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 542
Release: 2021-08-23
Genre: Mathematics
ISBN: 3110566656

Download Identical Relations in Lie Algebras Book in PDF, ePub and Kindle

This updated edition of a classic title studies identical relations in Lie algebras and also in other classes of algebras, a theory with over 40 years of development in which new methods and connections with other areas of mathematics have arisen. New topics covered include graded identities, identities of algebras with actions and coactions of various Hopf algebras, and the representation theory of the symmetric and general linear group.


Complex Algebraic Foliations

Complex Algebraic Foliations
Author: Alcides Lins Neto
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 249
Release: 2020-02-24
Genre: Mathematics
ISBN: 3110602059

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This book is a basic reference in the modern theory of holomorphic foliations, presenting the interplay between various aspects of the theory and utilizing methods from algebraic and complex geometry along with techniques from complex dynamics and several complex variables. The result is a solid introduction to the theory of foliations, covering basic concepts through modern results on the structure of foliations on complex projective spaces.


Complementation of Normal Subgroups

Complementation of Normal Subgroups
Author: Joseph Kirtland
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 156
Release: 2017-09-11
Genre: Mathematics
ISBN: 3110480212

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Starting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups. The contents cover a wide range of material from reduction theorems and subgroups in the derived and lower nilpotent series to abelian normal subgroups and formations. Contents Prerequisites The Schur-Zassenhaus theorem: A bit of history and motivation Abelian and minimal normal subgroups Reduction theorems Subgroups in the chief series, derived series, and lower nilpotent series Normal subgroups with abelian sylow subgroups The formation generation Groups with specific classes of subgroups complemented


Pre-Riesz Spaces

Pre-Riesz Spaces
Author: Anke Kalauch
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 314
Release: 2018-11-19
Genre: Mathematics
ISBN: 3110475448

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This monograph develops the theory of pre-Riesz spaces, which are the partially ordered vector spaces that embed order densely into Riesz spaces. Concepts from Riesz space theory such as disjointness, ideals, and bands are extended to pre-Riesz spaces. The analysis revolves around embedding techniques, including the Riesz completion and the functional representation. In the same spirit, norms and topologies on a pre-Riesz space and their extensions to the Riesz completion are examined. The generalized concepts are used to investigate disjointness preserving operators on pre-Riesz spaces and related notions. The monograph presents recent results as well as being an accessible introduction to the theory of partially ordered vector spaces and positive operators. Contents A primer on ordered vector spaces Embeddings, covers, and completions Seminorms on pre-Riesz spaces Disjointness, bands, and ideals in pre-Riesz spaces Operators on pre-Riesz spaces