A bound on element orders in the holomorph of a finite group

Abstract

Let $G$ be a finite group. We prove a theorem implying that the orders of elements of the holomorph $\mathrm{Hol}(G)$ are bounded from above by $|G|$, and we discuss an application to bounding automorphism orders of finite groups.

5 pages

References in corpus (2)

• Classification of finite group automorphisms with a large cycle
• Cycle lengths in finite groups and the size of the solvable radical