On locally graded groups with an Engel condition on infinite subsets |
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| Authors: | P Longobardi |
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| Institution: | Università degli Studi di Napoli “Federico II”, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Via Cintia – Monte S. Angelo, 80126 Napoli, Italy, IT
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| Abstract: | A group G is said to be in Ek*E_k^* (k a positive integer), if every infinite subset of G contains a pair of elements that generate a k-Engel group.¶It is shown that a finitely generated locally graded group G in Ek*E_k^* is a finite-by- (k-Engel) group, in particular a finite extension of a k-Engel group. |
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