Quotient Groups of Groups of Certain Classes - Trebenko, D. Ya.; Chernikov, N. S. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
For an arbitrary variety \(X\) of groups and an arbitrary class \(Y\) of groups that is closed on quotient groups, we prove that a quotient group G/N of the group G possesses an invariant system with \(X\) - and \(Y\) -factors (respectively, is a residually \(Y\) -group) if G possesses an invariant system with \(X\) - and \(Y\) -factors (respectively, is a residually \(Y\) -group) and N ∈ \(X\) (respectively, N is a maximal invariant \(X\) -subgroup of the group G).