Metacyclic Groups And The D(2) Problem
Metacyclic Groups And The D(2) Problem

Author: Francis E A Johnson

Publisher: World Scientific

Published: 2021-01-04

Total Pages: 372

ISBN-13: 9811222770

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The D(2) problem is a fundamental problem in low dimensional topology. In broad terms, it asks when a three-dimensional space can be continuously deformed into a two-dimensional space without changing the essential algebraic properties of the spaces involved.The problem is parametrized by the fundamental group of the spaces involved; that is, each group G has its own D(2) problem whose difficulty varies considerably with the individual nature of G.This book solves the D(2) problem for a large, possibly infinite, number of finite metacyclic groups G(p, q). Prior to this the author had solved the D(2) problem for the groups G(p, 2). However, for q > 2, the only previously known solutions were for the groups G(7, 3), G(5, 4) and G(7, 6), all done by difficult direct calculation by two of the author's students, Jonathan Remez (2011) and Jason Vittis (2019).The method employed is heavily algebraic and involves precise analysis of the integral representation theory of G(p, q). Some noteworthy features are a new cancellation theory of modules (Chapters 10 and 11) and a simplified treatment (Chapters 5 and 12) of the author's theory of Swan homomorphisms.

A Course on Finite Groups
A Course on Finite Groups

Author: H.E. Rose

Publisher: Springer Science & Business Media

Published: 2009-12-16

Total Pages: 314

ISBN-13: 1848828896

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Introduces the richness of group theory to advanced undergraduate and graduate students, concentrating on the finite aspects. Provides a wealth of exercises and problems to support self-study. Additional online resources on more challenging and more specialised topics can be used as extension material for courses, or for further independent study.

Groups of Prime Power Order
Groups of Prime Power Order

Author: Yakov G. Berkovich

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2015-12-14

Total Pages: 475

ISBN-13: 3110381559

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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.

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

Published: 2018-06-25

Total Pages: 410

ISBN-13: 3110533146

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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 5
Groups of Prime Power Order. Volume 5

Author: Yakov G. Berkovich

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2016-01-15

Total Pages: 434

ISBN-13: 3110295350

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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.

Blocks of Finite Groups and Their Invariants
Blocks of Finite Groups and Their Invariants

Author: Benjamin Sambale

Publisher: Springer

Published: 2014-11-19

Total Pages: 246

ISBN-13: 3319120069

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Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods. In a powerful combination, these tools are applied to solve many special cases of famous open conjectures in the representation theory of finite groups. Most of the material is drawn from peer-reviewed journal articles, but there are also new previously unpublished results. In order to make the text self-contained, detailed proofs are given whenever possible. Several tables add to the text's usefulness as a reference. The book is aimed at experts in group theory or representation theory who may wish to make use of the presented ideas in their research.