Order of elements in the groups related to the general linear group

AbstractFor a natural number n and a prime power q the general, special, projective general and projective special linear groups are denoted by GLn(q), SLn(q), PGLn(q) and PSLn(q), respectively. Using conjugacy classes of elements in GLn(q) in terms of irreducible polynomials over the finite field GF(q) we demonstrate how the set of order elements in GLn(q) can be obtained. This will help to find the order of elements in the groups SLn(q), PGLn(q) and PSLn(q). We also show an upper bound for the order of elements in SLn(q)