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FINITELY GENERATED SOLUBLE GROUPS WITH A CONDITION ON INFINITE SUBSETS

Published online by Cambridge University Press:  13 June 2012

ASADOLLAH FARAMARZI SALLES*
Affiliation:
Department of Mathematics, Damghan University, Damghan, Iran (email: [email protected])
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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 xy,[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().

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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