Khukhro, Evgeny and Shumyatsky, Pavel
(2018)
Finite groups with Engel sinks of bounded rank.
Glasgow Mathematical Journal, 60
(3).
pp. 695701.
ISSN 00170895
Full content URL: https://doi.org/10.1017/S0017089517000404
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Abstract
For an element g of a group G, an Engel sink is a subset E(g) such that for every x∈G all sufficiently long commutators [...[[x,g],g],…,g] belong to 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.
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