The Engel graph of a finite group G, denoted Gamma(G), is a directed graph encoding the pairs of elements in G satisfying some Engel word. Recent work of Detomi, Lucchini and Nemmi shows that Gamma(G) is connected and the problem of understanding the strong connectivity of this graph has been reduced to the case where G is an almost simple group. In this paper, we complete the analysis by determining when Gamma(G) is strongly connected in the almost simple setting; the only exceptions involve groups with socle PSL2(q) or 2B2(q).
The Engel graph of almost simple groups
Lucchini A.;
2025
Abstract
The Engel graph of a finite group G, denoted Gamma(G), is a directed graph encoding the pairs of elements in G satisfying some Engel word. Recent work of Detomi, Lucchini and Nemmi shows that Gamma(G) is connected and the problem of understanding the strong connectivity of this graph has been reduced to the case where G is an almost simple group. In this paper, we complete the analysis by determining when Gamma(G) is strongly connected in the almost simple setting; the only exceptions involve groups with socle PSL2(q) or 2B2(q).
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
