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AbstractA group G is locally graded if every finitely generated nontrivial subgroup of G has a nontrivial finite image. Let N (2, k)* denote the class of groups in which every infinite subset contains a pair of elements that generate a nilpotent subgroup of class at most k. We show that if G is a finitely generated locally graded N (2, k)*-group, then there is a positive integer c depending only on k such that G/Zc (G) is finite.
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics – Cambridge University Press
Published: Apr 9, 2009
Keywords: primary 20F19; 20E26; Infinite; nilpotent; groups; locally graded
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