Zassenhaus conjecture for cyclic-by-abelian groups

TL;DR

This paper proves the Zassenhaus Conjecture for a new class of groups called cyclic-by-abelian groups, extending previous results for nilpotent and metacyclic groups.

Contribution

It establishes the conjecture for cyclic-by-abelian groups, a significant extension in the understanding of torsion units in integral group rings.

Findings

Proves the Zassenhaus Conjecture for cyclic-by-abelian groups

Extends known results to a broader class of groups

Supports the conjecture's validity in more complex group structures

Abstract

Zassenhaus Conjecture for torsion units states that every augmentation one torsion unit of the integral group ring of a finite group G is conjugate to an element of G in the units of rational group algebra QG. This conjecture has been proved for nilpotent groups, metacyclic groups and some other families of groups. We prove the conjecture for cyclic-by-abelian groups.