For a finite group G, we investigate the directed graph gamma(G), whose vertices are the non-hypercentral elements of G and where there is an edge x ? y if and only if [x,(n) y] = 1 for some n is an element of N. We prove that gamma(G) is always weakly connected and is strongly connected if G/Z(infinity)(G) is neither Frobenius nor almost simple.
The Engel graph of a finite group
Detomi E.;Lucchini A.;Nemmi D.
2023
Abstract
For a finite group G, we investigate the directed graph gamma(G), whose vertices are the non-hypercentral elements of G and where there is an edge x ? y if and only if [x,(n) y] = 1 for some n is an element of N. We prove that gamma(G) is always weakly connected and is strongly connected if G/Z(infinity)(G) is neither Frobenius nor almost simple.File in questo prodotto:
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