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.