On Conjugacy And Order Structure Of Certain Classes Of Finite Groups

Abstract

The classification of finite groups still remains an open problem. The concept of conjugacy provides an insight on the structure of finite groups. It is an equivalence relation which provides a neat algebraic description of the size of each conjugacy class in a finite group. We set to examine the conjugacy and order structures of general linear groups, GL(n, q) and special linear groups, SL(n, q) with some restrictions on n. We have also established the special cases of conjugacy classes of GL(n, q) splitting in SL(n, q) and given the conditions of splitting or not splitting.