On Finite Extensions of FC-Groups in the Class of NF-Groups

• 来源期刊: 代数集刊（英文版）
• 关键词: FC-groups FC-by-finite finite-by-abelian finite-by-nilpotent nilpotent-by-finite
• 年，卷（期）: 2019,（1）
• 页码范围: 23-30
• 页数: 8页
• 语种: 英文
• DOI: 10.1142/S100538671900004X

摘要

Let F,N,A and N2 denote the properties of being finite,nilpotent,abelian and nilpotent of classes at most 2,respectively.Firstly we consider the class of finitely generated FN-groups.We show that the property FC is closed under finite extensions,and extend this result to finitely generated NF-groups.Secondly we prove that a finitely generated NF-group G is in the class ((FC)F,∞) if and only if G is an FA-group.Finally we prove that a finitely generated NF-group in the class ((FC)F,oo)* is an FN2-group.Moreover,G/Z2(G) is finite.