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FINITELY GENERATED SOLUBLE GROUPS WITH A CONDITION ON INFINITE SUBSETS
Published online by Cambridge University Press: 13 June 2012
Abstract
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(∞).
MSC classification
- 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