A note on the conjugacy problem for finite Sylow subgroups of linear pseudofinite groups

Abstract

We prove the conjugacy of Sylow 2-subgroups in pseudofinite (sic)(c) (in particular linear) groups under the assumption that there is at least one finite Sylow 2 -subgroup. We observe the importance of the pseudofiniteness assumption by analyzing an example of a linear group with nonconjugate finite Sylow 2-subgroups, which was constructed by Platonov.