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Locally graded groups with a nilpotency condition on infinite subsets
Published online by Cambridge University Press: 09 April 2009
Abstract
A 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.
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 69 , Issue 3 , December 2000 , pp. 415 - 420
- Copyright
- Copyright © Australian Mathematical Society 2000
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