On conjugacy classes of the F4 group over a field q with characteristic 2


This article continues a series of papers devoted to solving the problem by which a non-identity conjugacy class in a finite simple non-abelian group contains commuting elements. Previously, this statement was tested for sporadic, projective, alternating groups and some exceptional groups. In this article, the validity of the above-mentioned statement for the series exceptional groups 2F4(q) has been verified. After some basic definitions two theorems were proved. The former said about the content of commuting elements in the group, the latter did about the presence of conjugation of a semisimple element with its inverse. Then classes of unipotent and mixed elements were considered. The investigative techniques used were recommended for testing the general hypothesis when dealing with other groups.