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FINITELY GENERATED SOLUBLE GROUPS WITH A CONDITION ON INFINITE SUBSETS

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  13 June 2012

ASADOLLAH FARAMARZI SALLES
ASADOLLAH FARAMARZI SALLES*
Affiliation:
Department of Mathematics, Damghan University, Damghan, Iran (email: faramarzi@du.ac.ir)
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Abstract

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Let G be a group. We say that G∈𝒯(∞) provided that every infinite set of elements of G contains three distinct elements x,y,z such that x≠y,[x,y,z]=1=[y,z,x]=[z,x,y]. We use this to show that for a finitely generated soluble group G, G/Z2(G) is finite if and only if G∈𝒯(∞).

Keywords

finitely generated groupsnilpotent groupssoluble groups

MSC classification

Secondary: 20F19: Generalizations of solvable and nilpotent groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 152 - 157
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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