Irredundant bases for finite groups of Lie type

TL;DR

This paper establishes that the maximum length of an irredundant base for primitive actions of finite simple groups of Lie type grows polynomially with the group's rank, providing tight bounds and examples.

Contribution

It proves a polynomial upper bound on irredundant base length for these groups and demonstrates the bound's optimality with examples.

Findings

Maximum irredundant base length is polynomial in the group's rank.

The established upper bound is shown to be tight with explicit examples.

Provides a new understanding of the structure of finite groups of Lie type.

Abstract

We prove that the maximum length of an irredundant base for a primitive action of a finite simple group of Lie type is bounded above by a function which is a polynomial in the rank of the group. We give examples to show that this type of upper bound is best possible.