The Representations of GL(3,q), GL(4,q), PGL(3,q), and PGL(4,q)

This paper is a result of an investigation into general methods of determining the irreducible characters of GL( n, q ), the group of all non-singular linear substitutions with marks in GF( q ), and of the related groups, SL( n, q ), PGL( n, q ), PSL( n, q ), the corresponding group of determinant unity, projective group, projective group of determinant unity, respectively.