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Groups covered by finitely many nilpotent subgroups

Published online by Cambridge University Press:  17 April 2009

Gérard Endimioni
Gérard Endimioni
Affiliation:
Université de ProvenceUFR-MIM URA-CNRS 225 3 place Victor Hugo F-13331 Marseille Cedex 3, France
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Abstract

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Let G be a finitely generated soluble group. Lennox and Wiegold have proved that G has a finite covering by nilpotent subgroups if and only if any infinite set of elements of G contains a pair {x, y} such that (x, y) is nilpotent. The main theorem of this paper is an improvement of the previous result: we show that G has a finite covering by nilpotent subgroups if and only if any infinite set of elements of G contains a pair {x, y} such that [x, ny] = 1 for some integer n = n(x, y) ≥ 0.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 3 , December 1994 , pp. 459 - 464
Copyright
Copyright © Australian Mathematical Society 1994

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