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Coherent groups of units of integral group rings and direct products of free groups

Published online by Cambridge University Press:  28 June 2016

ÁNGEL DEL RÍO  and
PAVEL ZALESSKII
ÁNGEL DEL RÍO
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, 30100, Murcia, Spain. e-mail: adelrio@um.es
PAVEL ZALESSKII
Affiliation:
Departamento de Matemática, Universidade de Brasília, 70.910-900, Brasilia-DF, Brasil. e-mail: pz@mat.unb.br
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Abstract

We classify the finite groups G for which $\mathcal{U}({\mathbb Z} G)$, the group of units of the integral group ring of G, does not contain a direct product of two non-abelian free groups. This list of groups contains all the groups for which $\mathcal{U}({\mathbb Z} G)$ is coherent. This reduces the problem to classify the finite groups G for which $\mathcal{U}({\mathbb Z} G)$ is coherent to decide about the coherency of a finite list of groups of the form SLn(R), with R an order in a finite dimensional rational division algebra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 162 , Issue 2 , March 2017 , pp. 191 - 209
Copyright
Copyright © Cambridge Philosophical Society 2016 

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