Subgroup separability in integral group rings

Abstract

We give a list of finite groups containing all finite groups $G$ such that the group of units $\mathbb{Z}{G}^{\ast }$ of the integral group ring $\mathbb{Z}G$ is subgroup separable. There are only two types of these groups $G$ for which we cannot decide wether $Z{G}^{\ast }$ is subgroup separable, namely the central product $Q_{8}Y{D}_8$ and $Q_8\times C_{p}withp\text{prime and}p\equiv -1\mathrm{mod}(8)$.

9 pages

References in corpus (1)

• Developments on the congruence subgroup problem after the work of Bass, Milnor and Serre