Unit groups of group rings
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Unit groups of group rings

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Published by Longman Scientific & Technical in London .
Written in English

Subjects:

  • Groups, Theory of.

Book details:

Edition Notes

Statementby Gregory Karpilovsky.
SeriesPitman monographs and surveys in pure and applied mathematics -- 47
Classifications
LC ClassificationsQA171
The Physical Object
Pagination(312)p.
Number of Pages312
ID Numbers
Open LibraryOL15071945M
ISBN 100582023416

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Part 6 Rings with cyclic unit groups: finite commutative rings with a cyclic group of units: rings with a cyclic group of units - the general case. Part 7 Finite generation of unit groups: general results; finitely generated extensions; the Whitehead group and stability theorem; finite generation of GL n(R). Group algebras occur naturally in the theory of group representations of finite groups. The group algebra K[G] over a field K is essentially the group ring, with the field K taking the place of the ring. As a set and vector space, it is the free vector space on G over the field K. That is, for x in K[G]. Part 8 Unit groups of group rings: definitions and elementary properties-- trace of idempotents-- units of finite order-- trivial units-- conjugacy of group bases-- torsion-free complements-- units in commutative group rings. (Part contents). (source: Nielsen Book Data) Summary This book draws together four areas of mathematics - ring theory. Introduction to Groups, Rings and Fields HT and TT H. A. Priestley 0. Familiar algebraic systems: review and a look ahead. GRF is an ALGEBRA course, and .

This leads to the study of group algebras of virtually abelian groups and their representations as subalgebras of suitable matrix rings, where we develop a determinant condition for units in such. The object of this paper is to survey the results on the upper central series of the unit groups of integral group rings. View. for the unit groups of group rings like the characterization of Author: Vikas Bist. XVIII GROUPS OF UNITS IN RINGS An important field of application of abelian groups is the theory of multiplicative groups of commutative fields and, more generally, the groups of units in commutative and associative rings with identity. [In this chapter, both associativity and . The existence of free subgroups in the unit groups of group rings of finite groups was established in Recently a book was published Our intention is to continue the study of the structure of the unit group of integral group rings, with possible generalizations to unit groups of orders, and, in particular, to consider the Zassenhaus.

Jun 01,  · Let G be an abelian group, R a commutative ring of prime characteristic p with identity and R t G a commutative twisted group ring of G over happyplacekidsgym.come p is a fixed prime, G p and S(R t G) are the p-components of G and of the unit group U(R t G) of R t G, happyplacekidsgym.com R* be the multiplicative group of R and let f α (S) be the α-th Ulm-Kaplansky invariant of S(R t G) where α is any happyplacekidsgym.com: Todor Zh. Mollov, Nako A. Nachev. “This book is concerned with one of the main directions in the study of group rings, namely, questions around group identities satisfied by units . This is a nicely written book, understanding of which requires familiarity with groups and rings on the level of introductory graduate courses. Abstract. Let A be a torsion free abelian group and let G be the group of its automorphisms. Hallett and Hirsch proved that, if G is finite then G has to be a subdirect product of some copies of 6 explicitly distinguished small groups.. Our aim here is to extend this result to the case when G is periodic. We proceed in the context of rings and their groups of unitsCited by: 2. group there seems no obvious reason why one cannot have an infinite chain of larger and larger sporadic groups, each of which has a double cover that is a centralizer of an involution in the next one. Because of this problem (among others), it was unclear until quite late in the classification whether there would be a finite or infinite.