Minimal permutation representations for ${\rm GL}_2(\mathbb F_q)$

TL;DR

This paper classifies all smallest possible permutation representations of the group ${ m GL}_2( extbf{F}_q)$, providing a complete understanding of how this group can act on sets.

Contribution

It explicitly determines all minimal permutation representations of ${ m GL}_2( extbf{F}_q)$, a problem not previously fully resolved.

Findings

Complete classification of minimal permutation representations.

Identification of the smallest sets on which ${ m GL}_2( extbf{F}_q)$ acts faithfully.

Provides a foundation for understanding permutation actions of ${ m GL}_2( extbf{F}_q)$.

Abstract

In this paper we determine all minimal permutation representations of ${\rm GL}_2(\mathbb F_q)$.