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.
Dalla Volta, F., Mastrogiacomo, F., Spiga, P. (2024). On the strong connectivity of the 2-Engel graphs of almost simple groups. JOURNAL OF GROUP THEORY, 27(2), 297-312 [10.1515/jgth-2023-0060].
On the strong connectivity of the 2-Engel graphs of almost simple groups
Dalla Volta F.
;Mastrogiacomo F.;Spiga P.
2024
Abstract
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.
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