Finite groups with Engel sinks of bounded rank

Khukhro, Evgeny and Shumyatsky, Pavel (2018) Finite groups with Engel sinks of bounded rank. Glasgow Mathematical Journal, 60 (3). pp. 695-701. ISSN 0017-0895

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.

Keywords:Finite groups, Engel condition, nilpotent residual, bounded rank
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:29888
Deposited On:05 Dec 2017 20:33

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