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Metacyclic Groups And The D2 Problem
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Book Synopsis Metacyclic Groups And The D(2) Problem by : Francis E A Johnson
Download or read book Metacyclic Groups And The D(2) Problem written by Francis E A Johnson and published by World Scientific. This book was released on 2021-01-04 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :FRANCIS E A. JOHNSON Publisher :World Scientific Publishing Company ISBN 13 :9789811222757 Total Pages :280 pages Book Rating :4.2/5 (227 download)
Book Synopsis Metacyclic Groups And The D(2) Problem by : FRANCIS E A. JOHNSON
Download or read book Metacyclic Groups And The D(2) Problem written by FRANCIS E A. JOHNSON and published by World Scientific Publishing Company. This book was released on 2021-01-15 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The D(2)-Problem for Some Metacyclic Groups by : Jason Marcus Vittis
Download or read book The D(2)-Problem for Some Metacyclic Groups written by Jason Marcus Vittis and published by . This book was released on 2019 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study problems relating to the D(2)-problem for metacyclic groups of type G(p,p-1) for p an odd prime. Specifically we build on J Nadim"s work, which showed that over the integral group ring of G(5,4), the module of integers (upon which the group acts trivially) admits a diagonal resolution and a minimal representative for the third syzygy is R(2)+[y-1). Motivated by this result, we show that R(2)+[y-1) is both full and straight over the integral group ring of G(p,p-1) where p is any odd prime. Given FEA Johnson"s work on the D(2)-problem, this immediately leads to the conclusion that G(5,4) satisfies the D(2)-property, as well as providing a sufficient condition for the D(2)-property to hold for G(p,p-1), namely the condition that R(2)+[y-1) is a minimal representative for the third syzygy. Following this result, we prove a theorem, which in tandem with work from FEA Johnson relating to the module R(2) significantly simplifies the calculations required to show that R(2)+[y-1) is a minimal representative for the third syzygy. Finally, we carry out these calculations for the group G(7,6) and prove that G(7,6) satisfies the D(2)-property.
Book Synopsis Metacyclic Groups of Odd Order by : Hyo-Seob Sim
Download or read book Metacyclic Groups of Odd Order written by Hyo-Seob Sim and published by . This book was released on 1992 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Course on Finite Groups by : H.E. Rose
Download or read book A Course on Finite Groups written by H.E. Rose and published by Springer Science & Business Media. This book was released on 2009-12-16 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Degrees of Irreducible Representations of Metacyclic Groups by : Hyo-Seob Sim
Download or read book Degrees of Irreducible Representations of Metacyclic Groups written by Hyo-Seob Sim and published by . This book was released on 1992 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Groups of Prime Power Order by : Yakov G. Berkovich
Download or read book Groups of Prime Power Order written by Yakov G. Berkovich and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-12-14 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Groups of Prime Power Order. Volume 6 by : Yakov G. Berkovich
Download or read book Groups of Prime Power Order. Volume 6 written by Yakov G. Berkovich and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-06-25 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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Book Synopsis Groups of Prime Power Order. Volume 5 by : Yakov G. Berkovich
Download or read book Groups of Prime Power Order. Volume 5 written by Yakov G. Berkovich and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-01-15 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Equations written by and published by CUP Archive. This book was released on with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Blocks of Finite Groups and Their Invariants by : Benjamin Sambale
Download or read book Blocks of Finite Groups and Their Invariants written by Benjamin Sambale and published by Springer. This book was released on 2014-11-19 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Transactions of the American Mathematical Society by : American Mathematical Society
Download or read book Transactions of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1991 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Compositio Mathematica written by and published by . This book was released on 1951 with total page 952 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of the ... Symposium on Ring Theory by :
Download or read book Proceedings of the ... Symposium on Ring Theory written by and published by . This book was released on 1993 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Notices of the American Mathematical Society by : American Mathematical Society
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1972 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains articles of significant interest to mathematicians, including reports on current mathematical research.
