Schur’s exponent conjecture and related problems

Abstract: Assume $G$ is a finite $p$-group, and let $S$ be a Sylow $p$-subgroup of $\operatorname{Aut}(G)$ with $\operatorname{exp}(S) = q$. We prove that if $G$ is of class at most $p^{2} − 1$, then $\operatorname{exp}(G) \mid p^{2} q^{3}$, and if $G$ is a metabelian $p$-group of class at most $2 p − 1$, then $\operatorname{exp}(G) \mid p q^{3}$. To obtain this result, we will first speak about Schur’s exponent conjecture and related problems. This is joint work with my PhD student P. Komma.

group theory

Audience: researchers in the topic

GOThIC - Ischia Online Group Theory Conference

Series comments: Please send a message to andrea.caranti@unitn.it to receive a link to the Zoom room where the conference (a series of talks, actually) takes place.