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

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...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 2017-03, Vol.162 (2), p.191-209
Main Authors: DEL RÍO, ÁNGEL, ZALESSKII, PAVEL
Format: Article
Language:English
Subjects:
Algebra
Classification
Coherence
Integrals
Lists
Mathematical analysis
Rings (mathematics)
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Summary: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 SL n (R), with R an order in a finite dimensional rational division algebra.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004116000517