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

2021/12/02 by Komma, P., Thomas, V. Z.
#20B05 \sep 20D15 \sep 20F14 \sep 20F18 \sep 20G10 \sep 20J05 \sep 20J06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2112.01024

Abstract

Assume G is a finite p-group, and let S be a Sylow p-subgroup of Aut(G) with exp(S)=q. We prove that if G is of class c, then exp(G)|p^\ceillog_pcq³, and if G is a metabelian p-group of class at most 2p-1, then exp(G)|pq³.

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