Group rings with metabelian unit groups

Let F be a field of odd characteristic and G a group. In 1991 Shalev established necessary and sufficient conditions so that the unit group of the group ring FG is metabelian when G is finite. Here, in the modular case, we do the same without restrictions on G. In particular, new cases emerge when G...

Full description

Saved in:
Bibliographic Details
Published inJournal of pure and applied algebra Vol. 226; no. 6; p. 106946
Main Authors Juhász, Tibor, Spinelli, Ernesto
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2022
Subjects
Derived length
Group rings
Unit group
Derived length
16S34
16U60
Group rings
Unit group
Online AccessGet full text

Cover

More Information
Summary:Let F be a field of odd characteristic and G a group. In 1991 Shalev established necessary and sufficient conditions so that the unit group of the group ring FG is metabelian when G is finite. Here, in the modular case, we do the same without restrictions on G. In particular, new cases emerge when G contains elements of infinite order.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2021.106946