Finite groups with Engel sinks of bounded rank

2017/07/13 by Khukhro, E. I., Shumyatsky, P. · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1707.04187

Abstract

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.

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• Local--global generation property of commutators in finite π-soluble groups

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