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Locally graded groups with a nilpotency condition on infinite subsets

Part of: Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Costantino Delizia ,
Akbar Rhemtulla  and
Howard Smith
Costantino Delizia
Affiliation:
Universitá di Napoli ‘Federico II’ Dipartimento di Mathematica e Applicazioni Via Cintia - Monte S.Angelo, 80126 NapoliItaly e-mail: deliziac@matna2.dma.unina.it
Akbar Rhemtulla
Affiliation:
Department of Mathematical Sciences University of AlbertaEdmonton AlbertaCanadaT6G 2G1 e-mail: akbar@malinidi.math.ualberta.ca
Howard Smith
Affiliation:
Department of Mathematics Bucknell University LewisburgPA 17837USA e-mail: howsmith@bucknell.edu
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Abstract

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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.

Keywords

Infinitenilpotentgroupslocally graded

MSC classification

Secondary: 20F19: Generalizations of solvable and nilpotent groups 20E26: Residual properties and generalizations; residually finite groups
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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