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Infinite locally soluble k -Engel groups

Lucia Serena Spiezia (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we deal with the class E k * of groups G for which whenever we choose two infinite subsets X , Y there exist two elements x X , y Y such that x , y , , y k = 1 . We prove that an infinite finitely generated soluble group in the class E k * is in the class E k of k -Engel groups. Furthermore, with k = 2 , we show that if G E 2 * is infinite locally soluble or hyperabelian group then G E 2 .

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