{ "id": "2205.14984", "version": "v1", "published": "2022-05-30T10:34:18.000Z", "updated": "2022-05-30T10:34:18.000Z", "title": "The Engel graph of almost simple groups", "authors": [ "Andrea Lucchini", "Pablo Spiga" ], "categories": [ "math.GR", "math.CO" ], "abstract": "Given a finite group $G$, the Engel graph of $G$ 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 $G$ 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.", "revisions": [ { "version": "v1", "updated": "2022-05-30T10:34:18.000Z" } ], "analyses": { "keywords": [ "engel graph", "strongly connectivity", "finite non-abelian simple groups", "engel word", "directed graph encoding pairs" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable" } } }