Conjugacy classes of completely reducible cube-free solvable p′-subgroups of GL(2,q)

Abstract

Let [Formula: see text] be a cube-free positive integer and let [Formula: see text] be a prime such that [Formula: see text]. In this paper, we find the number of conjugacy classes of completely reducible solvable cube-free subgroups in [Formula: see text] of order [Formula: see text], where [Formula: see text] is a power of [Formula: see text].