Rank and subdegrees of PGL(2, q) acting cosets of PGL(2, e) for q an even power of e

Abstract

The action of projective general group on the cosets of its maximal subgroups has been studied. For instance, [9] studied the action of G on the cosets of P GL(2, e) when q is an odd prime power of e. In this paper, we determine the rank and subdegrees of the action of P GL(2, q) on the cosets of its subgroup P GL(2, e) for odd q and an even power of e. We apply the table of marks to achieve this.