Minimal permutation representations for linear groups

TL;DR

This paper investigates the smallest permutation representations that faithfully represent the linear groups SL_n(F_q) and GL_n(F_q), providing insights into their minimal permutation degrees.

Contribution

It introduces the concept of minimal faithful permutation representations specifically for SL_n(F_q) and GL_n(F_q), advancing understanding of their permutation structure.

Findings

Determined minimal degrees for SL_n(F_q) and GL_n(F_q)

Established bounds on permutation representation sizes

Compared minimal representations across different group parameters

Abstract

In this paper we study the minimal faithful permutation representations of $SL_n(\mathbb F_q)$ and $GL_n(\mathbb F_q)$.