Torsion Units in Integral Group Rings

Torsion units in integral group rings of Janko simple groups

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko simple groups. As a consequence, for the Janko groups J1, J2 and J3 we confirm Kimmerle’s conjecture on prime graphs.

Torsion Units in Integral Group Rings of Conway Simple Groups

Using the Luthar–Passi method, we investigate the possible orders and partial augmentations of torsion units of the normalized unit group of integral group rings of Conway simple groups Co1, Co2 and Co3. Let U(ZG) be the unit group of the integral group ring ZG of a finite group G, and V (ZG) be its normalized unit group

On the Torsion Units of Some Integral Group Rings∗

It is shown that any torsion unit of the integral group ring ZG of a finite group G is rationally conjugate to a trivial unit if G = P o A with P a normal Sylow p-subgroup of G and A an abelian p′-group (thus confirming a conjecture of Zassenhaus for this particular class of groups). The proof is an application of a fundamental result of Weiss. It is also shown that the Zassenhaus conjecture ho...

On Torsion Subgroups in Integral Group Rings of Finite Groups

A characterization of torsion units in integral group of ZS3

In this study, we give a characterization of all torsion units which are in the unit group of ZS3 integral group ring of symmetric group S3, and classify conjugate classes of these units. We used the group of all doubly stochastic matrices in GL(3,Z) in this classification. The investigation of torsion units is not restricted with this study, and the classification of torsion units of bigger or...