2013
DOI: 10.48550/arxiv.1309.0974
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On the Congruence Subgroup Problem for integral group rings

Abstract: Let G be a finite group, ZG the integral group ring of G and U(ZG) the group of units of ZG. The Congruence Subgroup Problem for U(ZG) is the problem of deciding if every subgroup of finite index of U(ZG) contains a congruence subgroup, i.e. the kernel of the natural homomorphism U(ZG) → U(ZG/mZG) for some positive integer m. The congruence kernel of U(ZG) is the kernel of the natural map from the completion of U(ZG) with respect to the profinite topology to the completion with respect to the topology defined … Show more

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