Virtually-residually-p automorphism groups of group rings
Let p be a prime. A group is virtually-residually-p if it contains a normal subgroup of finite index and which is residually a finite p-group. Let G be a finitely generated and virtually-residually-p group. Let R be a finitely generated ring with an identity having an ideal I whose index is a power of p and such that I is residually a finite nilpotent ring of additive p-power order. It is here shown that Aut R(G), the automorphism group of the group ring R(G) is virtually-residually-p. This result relates to work of the reviewer [Proc. Edinb. Math. Soc., II. Ser. 30, 207-213 (1987; Zbl 0602.16009)] and extends a result of \textit{A. Lubotzky} from groups to group rings [J. Algebra 63, 494-498 (1980; Zbl 0432.20025)].
finitely generated and virtually-residually-p group
scientific article; zbMATH DE number 4136141
scientific article