Modules over the Integral Group Ring of a Non-Abelian Group of Order $pq$

Modules over the Integral Group Ring of a Non-Abelian Group of Order $pq$ PDF

Author: Lee Klingler

Publisher: American Mathematical Soc.

Published: 1986

Total Pages: 138

ISBN-13: 0821823434

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By using pullbacks, we obtain a description of finitely generated modules over the integral group ring of a non-abelian group of order [italic]pq. The description is detailed enough to obtain information about the behavior of the modules in direct sums. We make the description more precise by relating it to the locally free class group of the integral group ring.

Methods in Module Theory

Methods in Module Theory PDF

Author: Abrams

Publisher: CRC Press

Published: 1992-10-16

Total Pages: 352

ISBN-13: 9780824788025

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A collection of articles embodying the work presented at the 1991 Methods in Module Theory Conference at the University of Colorado at Colorado Springs - facilitating the explanation and cross-fertilization of new techniques that were developed to answer a variety of module-theoretic questions.

Algebraic K-Theory: Connections with Geometry and Topology

Algebraic K-Theory: Connections with Geometry and Topology PDF

Author: John F. Jardine

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 563

ISBN-13: 9400923996

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A NATO Advanced Study Institute entitled "Algebraic K-theory: Connections with Geometry and Topology" was held at the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December 11 of 1987. This meeting was jointly supported by NATO and the Natural Sciences and Engineering Research Council of Canada, and was sponsored in part by the Canadian Mathematical Society. This book is the volume of proceedings for that meeting. Algebraic K-theory is essentially the study of homotopy invariants arising from rings and their associated matrix groups. More importantly perhaps, the subject has become central to the study of the relationship between Topology, Algebraic Geometry and Number Theory. It draws on all of these fields as a subject in its own right, but it serves as well as an effective translator for the application of concepts from one field in another. The papers in this volume are representative of the current state of the subject. They are, for the most part, research papers which are primarily of interest to researchers in the field and to those aspiring to be such. There is a section on problems in this volume which should be of particular interest to students; it contains a discussion of the problems from Gersten's well-known list of 1973, as well as a short list of new problems.

Metacyclic Groups And The D(2) Problem

Metacyclic Groups And The D(2) Problem PDF

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.

Advances in Algebra and Model Theory

Advances in Algebra and Model Theory PDF

Author: M Droste

Publisher: CRC Press

Published: 2019-08-16

Total Pages: 516

ISBN-13: 1000725278

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Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.

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