Groups Of Prime Power Order Volume 3

Author : Yakov Berkovich,Zvonimir Janko
Publisher : Walter de Gruyter
Page : 669 pages
File Size : 53,6 Mb
Release : 2011-06-30
Category : Mathematics
ISBN : 9783110254488

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Groups of Prime Power Order. Volume 3 by Yakov Berkovich,Zvonimir Janko Pdf

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.

Author : Yakov G. Berkovich,Zvonimir Janko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 406 pages
File Size : 43,7 Mb
Release : 2018-06-25
Category : Mathematics
ISBN : 9783110531008

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Yakov Berkovich; Zvonimir Janko: Groups of Prime Power Order by Yakov G. Berkovich,Zvonimir Janko Pdf

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 : Yakov G. Berkovich,Zvonimir Janko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 475 pages
File Size : 46,8 Mb
Release : 2015-12-14
Category : Mathematics
ISBN : 9783110281477

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Groups of Prime Power Order by Yakov G. Berkovich,Zvonimir Janko Pdf

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.

Author : Yakov G. Berkovich,Zvonimir Janko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 433 pages
File Size : 43,6 Mb
Release : 2016-01-15
Category : Mathematics
ISBN : 9783110295351

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Yakov Berkovich; Zvonimir Janko: Groups of Prime Power Order. Volume 5 by Yakov G. Berkovich,Zvonimir Janko Pdf

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 : Yakov Berkovich
Publisher : Walter de Gruyter
Page : 533 pages
File Size : 48,8 Mb
Release : 2008-12-10
Category : Mathematics
ISBN : 9783110208221

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Groups of Prime Power Order. Volume 1 by Yakov Berkovich Pdf

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.

Author : Yakov Berkovich,Zvonimir Janko
Publisher : Walter de Gruyter
Page : 613 pages
File Size : 54,7 Mb
Release : 2008-12-10
Category : Mathematics
ISBN : 9783110208238

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Groups of Prime Power Order. Volume 2 by Yakov Berkovich,Zvonimir Janko Pdf

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.

Author : Charles Richard Leedham-Green,Susan McKay
Publisher : Clarendon Press
Page : 356 pages
File Size : 53,9 Mb
Release : 2002
Category : Mathematics
ISBN : 0198535481

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The Structure of Groups of Prime Power Order by Charles Richard Leedham-Green,Susan McKay Pdf

An important monograph summarizing the development of a classification system of finite p-groups.

Author : Yuri Bahturin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 542 pages
File Size : 52,6 Mb
Release : 2021-08-23
Category : Mathematics
ISBN : 9783110566659

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Identical Relations in Lie Algebras by Yuri Bahturin Pdf

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.

Author : Helmut Strade
Publisher : Walter de Gruyter GmbH & Co KG
Page : 550 pages
File Size : 54,8 Mb
Release : 2017-04-24
Category : Mathematics
ISBN : 9783110515442

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Structure Theory by Helmut Strade Pdf

The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p > 0 is a long-standing one. Work on this question has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. Contents Toral subalgebras in p-envelopesLie algebras of special derivationsDerivation simple algebras and modulesSimple Lie algebrasRecognition theoremsThe isomorphism problemStructure of simple Lie algebrasPairings of induced modulesToral rank 1 Lie algebras

Author : Peter J. Cameron
Publisher : Oxford University Press on Demand
Page : 353 pages
File Size : 49,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9780198569138

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Introduction to Algebra by Peter J. Cameron Pdf

This Second Edition of a classic algebra text includes updated and comprehensive introductory chapters,new material on axiom of Choice, p-groups and local rings, discussion of theory and applications, and over 300 exercises. It is an ideal introductory text for all Year 1 and 2 undergraduate students in mathematics.

Author : I︠A︡. G. Berkovich,Zvonimir Janko
Publisher : ISSN
Page : 540 pages
File Size : 40,9 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015081460407

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Groups of Prime Power Order by I︠A︡. G. Berkovich,Zvonimir Janko Pdf

Main description: This is the first of three volumes on finite p-group theory. It presents the state of the art and in addition contains numerous new and easy proofs of famous theorems, many exercises (some of them with solutions), and about 1500 open problems. It is expected to be useful to certain applied mathematics areas, such as combinatorics, coding theory, and computer sciences. The book should also be easily comprehensible to students and scientists with some basic knowledge of group theory and algebra.

Author : American Mathematical Society
Publisher : Unknown
Page : 490 pages
File Size : 45,6 Mb
Release : 1945
Category : Mathematics
ISBN : IND:30000099714804

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Transactions of the American Mathematical Society by American Mathematical Society Pdf

Author : Anonim
Publisher : Unknown
Page : 356 pages
File Size : 53,8 Mb
Release : 2008
Category : Numerical analysis
ISBN : UOM:39015085197732

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Journal of Numerical Mathematics by Anonim Pdf

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 499 pages
File Size : 42,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789400959941

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

Author : Anonim
Publisher : Unknown
Page : 656 pages
File Size : 43,5 Mb
Release : 1968
Category : Mathematics
ISBN : UOM:39015057332796

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Bulletin of the American Mathematical Society by Anonim Pdf