Geodesic
FINITE GROUPS WITH ENGEL SINKS OF BOUNDED RANK
Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 695-701

Voir la notice de l'article provenant de la source Cambridge University Press

For an element g of a group G, an Engel sink is a subset ${\mathscr E}$(g) such that for every x ∈ G all sufficiently long commutators [. . .[[x, g], g], . . ., g] belong to ${\mathscr E}$(g). A finite group is nilpotent if and only if every element has a trivial Engel sink. We prove that if in a finite group G every element has an Engel sink generating a subgroup of rank r, then G has a normal subgroup N of rank bounded in terms of r such that G/N is nilpotent. 
KHUKHRO, E. I.; SHUMYATSKY, P. FINITE GROUPS WITH ENGEL SINKS OF BOUNDED RANK. Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 695-701. doi: 10.1017/S0017089517000404
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