Group rings and the RS-property

TL;DR

This paper investigates infinite groups whose integral group rings have only trivial central units, exploring the RS-property related to conjugacy, and aims to deepen understanding of the algebraic structure of such groups.

Contribution

It introduces and analyzes the RS-property in the context of infinite groups, linking conjugacy properties to the structure of their integral group rings.

Findings

Characterization of groups with the RS-property

Connection between conjugacy and trivial central units

Conditions under which the integral group ring has only trivial central units

Abstract

The object of this paper is to study (infinite) groups whose integral group rings have only trivial central units. This property is closely related to a property, here called the RS-property (\cite{DMS05}, \cite{RS90}), involving conjugacy in the group.