# New paper

E. I. Khukhro and P. Shumyatsky, *Almost Engel finite and profinite groups, *submitted, 2015;* *arXiv:1512.06097.

Abstract: Let be an element of a group . For a positive integer , let be the subgroup generated by all commutators over , where is repeated times. We prove that if is a profinite group such that for every there is such that is finite, then has a finite normal subgroup such that is locally nilpotent. The proof uses the Wilson–Zelmanov theorem saying that Engel profinite groups are locally nilpotent. In the case of a finite group , we prove that if, for some , for all , then the order of the nilpotent residual is bounded in terms of .

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