On the radical of group rings
Abstract
Abstract It is conjectured that, for any group G , the Jacobson radical $$J({\mathbb {Z}}[G])$$ J ( Z [ G ] ) of the integral group ring $${\mathbb {Z}}[G]$$ Z [ G ] is zero. This is known to be true when G is finite. Here we show it is true for a reasonably large class of infinite groups, including finitely generated linear groups and groups which satisfy Higman’s ‘two unique products’ condition.
Fields of Study & Subjects
Rings
Modules
and Algebras
Finite Group Theory Research
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Archiv der Mathematik
- Volume
- 126
- Issue
- 3
- Pages
- 239–246
- Publication date
- 7 January 2026
- Language
- EN