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29 March 2024
 
  » arxiv » 1707.4187

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Finite groups with Engel sinks of bounded rank
E. I. Khukhro ; P. Shumyatsky ;
Date 13 Jul 2017
AbstractFor an element $g$ of a group $G$, an Engel sink is a subset ${mathscr E}(g)$ such that for every $xin G$ all sufficiently long commutators $[...[[x,g],g],dots ,g]$ 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.
Source arXiv, 1707.4187
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