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

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DOI

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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     author = {KHUKHRO, E. I. and SHUMYATSKY, P.},
     title = {FINITE {GROUPS} {WITH} {ENGEL} {SINKS} {OF} {BOUNDED} {RANK}},
     journal = {Glasgow mathematical journal},
     pages = {695--701},
     year = {2018},
     volume = {60},
     number = {3},
     doi = {10.1017/S0017089517000404},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000404/}
}
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