【摘 要】
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We prove that a finitely generated soluble group G is nilpotent-by-finite (respectively, finite-by-nilpotent) if every infinite subset of G contains two element
【机 构】
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Département de Mathématiques, Faculté des Sciences Université Ferhat Abbas, Sétif 19000, Algérie
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We prove that a finitely generated soluble group G is nilpotent-by-finite (respectively, finite-by-nilpotent) if every infinite subset of G contains two elements x,y generating a nilpotent-by-finite (respectively, finite-by-nilpotent)group.Moreover,for a positive integer k,if we suppose is (nipotent of class k)-by-finite (respectively, finite-by-(nilpotent of class k)), then there is an integer c =c(k) such that G is (nilpotent of class c)-by-finite (respectively, finiteby-(nilpotent of class c)).
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