Torsion subgroups in the units of the integral group ring of PSL(2,p^3)

TL;DR

This paper proves that all prime order subgroups in the units of the integral group ring of PSL(2,p^3) are isomorphic to subgroups of PSL(2,p^3), answering a specific algebraic question.

Contribution

It establishes that for the groups considered, all prime order subgroups in the units are isomorphic to subgroups of the original group, confirming a conjecture for this case.

Findings

All r-subgroups in the units are isomorphic to subgroups of PSL(2,p^3)

Answers a specific open question in the theory of integral group rings

Provides structural insight into units of the group ring

Abstract

We show that for every prime $r$ all $r$-subgroups in the normalized units of the integral group ring of $\operatorname{PSL}(2,p^3)$ are isomorphic to subgroups of $\operatorname{PSL}(2,p^3)$. This answers a question of M. Hertweck, C.R. H\"ofert and W. Kimmerle for this series of groups.