Covering the set of $p$-elements in finite groups by Sylow $p$-subgroups

Abstract

Let $G_p$ be the set of $p$-elements of a finite group $G$. Do we need all the Sylow $p$-subgroups of $G$ to cover $G_p$? Although this question does not have an affirmative answer in general, our work indicates that the answer is yes more often than one could perhaps expect.

We fix two gaps pointed out by Gunter Malle in the proofs of Theorem D and Theorem 5.1 of the published version