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

TL;DR

This paper determines the number of conjugacy classes of certain cube-free solvable subgroups within GL(2, q), expanding understanding of subgroup structure in linear algebraic groups over finite fields.

Contribution

It provides a formula for counting conjugacy classes of completely reducible cube-free solvable p'-subgroups in GL(2, q).

Findings

Count of conjugacy classes for specified subgroups derived.

Results applicable to subgroup classification in linear algebraic groups.

Enhanced understanding of subgroup structures in GL(2, q).

Abstract

Let m be a cube-free positive integer and let p be a prime such that p does not divide m. In this paper we find the number of conjugacy classes of completely reducible solvable cube-free subgroups in GL(2, q) of order m, where q is a power of p.