Hall-Higman type theorems for exceptional groups of Lie type, I

TL;DR

This paper investigates the minimum polynomial degrees of p-elements in cross-characteristic representations of certain simple groups of exceptional Lie type, establishing that this degree equals the element's order for groups with BN-pair rank at most 2.

Contribution

It proves that for these groups, the minimum polynomial degree of p-elements matches their order, extending understanding of their representation theory.

Findings

Minimum polynomial degree equals element order for the specified groups.

Focus on groups with BN-pair rank at most 2.

Results contribute to representation theory of exceptional Lie type groups.

Abstract

The paper studies the minimum polynomial degrees of $p$-elements in cross-characteristic representations of simple groups of exceptional Lie type whose BN-pair rank is at most 2. Specifically, we prove that the degree in question equals the order of the element.