On Sylow Theory for Linear Pseudofinite Groups

Abstract

We prove the conjugacy of Sylow p-subgroups of linear pseudofinite groups under the assumption of the existence of a finite Sylow p-subgroup. We also construct an example which shows that this conjugacy result does not hold in general for linear pseudofinite groups. This result partially answers a question raised by Frank Wagner (see Remark 4.9).