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 FTV-groups. Wc show that the property ...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 FTV-groups. Wc 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, oo) if and only if G is an FA-group. Finally we prove that a finitely genera ted ATF-group in the class ((FC)F,∞)^* is an FM-group. Moreover, G/Z2(G) is finite.展开更多
文摘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 FTV-groups. Wc 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, oo) if and only if G is an FA-group. Finally we prove that a finitely genera ted ATF-group in the class ((FC)F,∞)^* is an FM-group. Moreover, G/Z2(G) is finite.
