The Structure of Groups of Prime Power Order

The Structure of Groups of Prime Power Order PDF Author: Charles Richard Leedham-Green
Publisher: Clarendon Press
ISBN: 9780198535485
Category : Mathematics
Languages : en
Pages : 356

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

Groups of Prime Power Order. Volume 2

Groups of Prime Power Order. Volume 2 PDF 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.

Groups of Prime Power Order. Volume 1

Groups of Prime Power Order. Volume 1 PDF Author: Yakov Berkovich
Publisher: Walter de Gruyter
ISBN: 3110208229
Category : Mathematics
Languages : en
Pages : 533

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Book Description
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 PDF Author: Yakov Berkovich
Publisher: Walter de Gruyter
ISBN: 3110254484
Category : Mathematics
Languages : en
Pages : 669

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Book Description
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 5

Groups of Prime Power Order. Volume 5 PDF Author: Yakov G. Berkovich
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110389045
Category : Mathematics
Languages : en
Pages : 497

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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.

Groups of Prime Power Order. Volume 6

Groups of Prime Power Order. Volume 6 PDF Author: Yakov G. Berkovich
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110531003
Category : Mathematics
Languages : en
Pages : 495

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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.

Groups of Prime Power Order. Volume 4

Groups of Prime Power Order. Volume 4 PDF Author: Yakov G. Berkovich
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110281473
Category : Mathematics
Languages : en
Pages : 476

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Book Description
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.

Theory of Groups of Finite Order

Theory of Groups of Finite Order PDF Author: William S. Burnside
Publisher: Courier Corporation
ISBN: 0486159442
Category : Mathematics
Languages : en
Pages : 545

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Book Description
Classic 1911 edition covers many group-related properties, including an extensive treatment of permutation groups and groups of linear substitutions, along with graphic representation of groups, congruence groups, and special topics.

Analytic Pro-P Groups

Analytic Pro-P Groups PDF 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.

Contemporary Abstract Algebra

Contemporary Abstract Algebra PDF Author: Joseph A. Gallian
Publisher: CRC Press
ISBN: 1000337332
Category : Mathematics
Languages : en
Pages : 654

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Book Description
Now in it's Tenth Edition, we acquire this course-market leader from Cengage US. Through the first nine editions, this has become the leading seller for the undergraduate Abstract Algebra course worldwide. The rollover potential alone is nearly 10,000 copies and might be more. Abstract Algebra is taught at every four year college and university with a mathematics department throughout the world. There are two primary audiences, mathematics majors and education majors hoping to teach. Both take this course, often together. • Best-seller in US, Canada, ROW • Author is now famous for this book, very active in US mathematics organizations including AMS and former president of MAA. • Book is known for motivational exposition, excellent and thorough exercises (much more than typically found in CRC textbooks), and alternative solutions to promote a range of approaches • Best seller since 3-4 edition • The full list of reviews since publication is well into the hundreds.