On the strong connectivity of the 2-Engel graphs of almost simple groups

F. Dalla Volta, F. Mastrogiacomo, P. Spiga

Published 2023-04-19Version 1

The Engel graph of a finite group $G$ is a directed graph encoding the pairs of elements in $G$ satisfying some Engel word. Recent work of Lucchini and the third author shows that, except for a few well-understood cases, the Engel graphs of almost simple groups are strongly connected. In this paper, we give a refinement to this analysis.