The Engel graph of almost simple groups
Andrea Lucchini, Pablo Spiga

TL;DR
This paper studies the strongly connectivity of Engel graphs in finite non-abelian simple groups, reducing the problem to understanding these graphs in simple groups, and providing new insights into their structure.
Contribution
It advances the understanding of Engel graphs by analyzing their strongly connectivity specifically in finite non-abelian simple groups, building on prior reductions.
Findings
Engel graph strongly connectivity characterized for simple groups
Reduction of general group problem to simple groups case
New structural properties of Engel graphs identified
Abstract
Given a finite group , the Engel graph of is a directed graph encoding pairs of elements satisfying some Engel word. From the work of Detomi, Lucchini and Nemmi, the strongly connectivity of the Engel graph of an arbitrary group is reduced to the understanding of the strongly connectivity of the Engel graph of non-abelian simple groups. In this paper, we investigate the strongly connectivity of the Engel graph of finite non-abelian simple groups.
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Taxonomy
TopicsFinite Group Theory Research · Cooperative Communication and Network Coding · Graphene research and applications
