Bounding the exponent of a finite group by the exponent of the automorphism group and a theorem of Schur

P. Komma, V. Z. Thomas

Assume $G$ is a finite $p$-group, and let $S$ be a Sylow $p$-subgroup of $\mathrm{Aut}(G)$ with $\exp (S)=q$. We prove that if $G$ is of class $c$, then $\exp(G)|p^{\ceil{\log…