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Locally graded groups with a nilpotency condition on infinite subsets

Locally graded groups with a nilpotency condition on infinite subsets 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics Cambridge University Press

Locally graded groups with a nilpotency condition on infinite subsets

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References (10)

Publisher
Cambridge University Press
Copyright
Copyright © Australian Mathematical Society 2000
ISSN
0263-6115
DOI
10.1017/S1446788700002536
Publisher site
See Article on Publisher Site

Abstract

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

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and StatisticsCambridge University Press

Published: Apr 9, 2009

Keywords: primary 20F19; 20E26; Infinite; nilpotent; groups; locally graded

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