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Finite groups with Engel sinks of bounded rank | E. I. Khukhro
; P. Shumyatsky
; | Date: |
13 Jul 2017 | Abstract: | For 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 | Services: | Forum | Review | PDF | Favorites |
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