Published January 1, 2018
| Version v1
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Bounded Engel elements in groups satisfying an identity
- 1. Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil
- 2. Ahi Evran Univ, Matemat Bolumu, TR-40100 Merkez, Kirsehir, Turkey
- 3. Univ Salerno, Dipartimento Matemat, Via Giovanni Paolo 2,132, I-84084 Fisciano, SA, Italy
Description
We prove that a residually finite group G satisfying an identity and generated by a commutator closed set X of bounded left Engel elements is locally nilpotent. We also extend such a result to locally graded groups, provided that X is a normal set. As an immediate consequence, we obtain that a locally graded group satisfying an identity, all of whose elements are bounded left Engel, is locally nilpotent.
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