Twisted Group Rings Whose Units Form an FC-Group

TL;DR

This paper characterizes the structure of the unit group in infinite twisted group algebras, focusing on FC-subgroups and conditions for finitely conjugacy classes, extending known theorems in group algebra theory.

Contribution

It provides a detailed description of the maximal FC-subgroup of units and characterizes units with finitely conjugacy classes in twisted group algebras, generalizing existing results.

Findings

Maximal FC-subgroup of units identified

Characterization of units with finitely many conjugacy classes

Extension of Cliff-Sehgal-Zassenhaus' theorem to twisted cases

Abstract

Let U be the group of units of an infinite twisted group algebra K_\lambda G over a field K. We describe the maximal FC-subgroup of U and give a characterization of U with finitely conjugacy classes. In the case of group algebras we obtain the Cliff-Sehgal-Zassenhaus' theorem.