$p$-subgroups of units in $\mathbb{Z}G$

TL;DR

This paper investigates whether Sylow-like theorems hold for units in integral group rings, confirming this for Frobenius groups and analyzing p-subgroups in simple groups using existing methods.

Contribution

It extends Sylow-like theorem results to integral group rings of Frobenius groups and explores p-subgroups in simple groups with known techniques.

Findings

Sylow-like theorem holds for Frobenius groups' integral group rings

Analysis of p-subgroups in projective linear simple groups

Completes previous work by other researchers

Abstract

We consider the question whether a Sylow like theorem is valid in the normalized units of integral group rings of finite groups. After a short survey on the known results we show that this is the case for integral group rings of Frobenius groups. This completes work of M.A. Dokuchaev, S.O. Juriaans and V. Bovdi and M. Hertweck. We analyze projective linear simple groups and show what can be achieved for p-subgroups with known methods.