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

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We classify the finite groups G for which U(ZG), 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 U(ZG) is coherent. This reduces the problem to classify the finite groups G for which U(ZG) 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.

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