Virtually-residually-p automorphism groups of group rings
type: Item
instance of: scholarly article
title: Virtually-residually-p automorphism groups of group rings
zbMATH Open document ID: 0694.16010
DOI: 10.1016/0021-8693(90)90103-U
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20B27
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 20E26
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 4136141
zbMATH Keywords: subgroup of finite index
zbMATH Keywords: finitely generated and virtually-residually-p group
zbMATH Keywords: nilpotent ring
zbMATH Keywords: automorphism group
zbMATH Keywords: group rings
author: James McCool
MaRDI profile type: Publication
cites work: Exactness properties of profinite completion functors
cites work: Automorphisms of groups and of schemes of finite type
cites work: Automorphism Groups of Residually Finite Groups
cites work: Residual Properties of Infinite Soluble Groups
cites work: Q5595230
cites work: Subrings of finite index in finitely generated rings
cites work: Normal automorphisms of free groups
cites work: On the centre and residual finiteness of the automorphism group of a group ring
cites work: Q5676405
Recommended article: On groups of automorphisms of residually finite groups
Recommended article: p -Groups, Lie p -Rings and p -Automorphisms
Recommended article: Q3218257
Recommended article: Q3331395
Recommended article: On the centre and residual finiteness of the automorphism group of a group ring
Recommended article: Rings related to automorphism groups
Recommended article: Q4016457
Recommended article: Q4716184
Recommended article: Class groups and automorphism groups of group rings
Recommended article: Q4226367
description: scientific article; zbMATH DE number 4136141