Dr. Asadollah Faramarzi
Assistant Professor
Finitely generated soluble groups with a condition on infinite subsets
ABSTRACT
Let G be a group. We say that G∈?(∞) 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/Z
2(G) is finite if and only if G∈?(∞).
2(G) is finite if and only if G∈?(∞).