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

Abstract

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