Pronormality of Hall subgroups in finite simple groups

TL;DR

This paper proves that Hall subgroups in finite simple groups are pronormal, confirming a long-standing problem and advancing understanding of subgroup structure in finite simple groups.

Contribution

It provides a proof that all Hall subgroups in finite simple groups are pronormal, resolving Problem 17.45(a) from the Kourovka notebook.

Findings

Hall subgroups in finite simple groups are pronormal

Resolved a problem from the Kourovka notebook

Enhances understanding of subgroup properties in finite simple groups

Abstract

We prove that Hall subgroups of finite simple groups are pronormal. Thus we obtain an affirmative answer to Problem 17.45(a) of "Kourovka notebook".