London Algebra Colloquium abstract

Element orders and Sylow structure

Gunter Malle (Kaiserslautern), 5th March 2009

Abstract

We show that in a finite group without elements of order pq (where p, q are two fixed distinct primes) either the Sylow p-subgroup or the Sylow q-subgroup is abelian, up to essentially one exception. The proof uses results on coprime group actions and the classification of finite simple groups.

This is joint work with A. Moreto and G. Navarro from Valencia.