Quotient Groups of Groups of Certain Classes

  • D. Ya. Trebenko
  • N. S. Chernikov

Abstract

For an arbitrary variety \(\mathfrak{X}\) of groups and an arbitrary class \(\mathfrak{Y}\) 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 \(\mathfrak{X}\) - and \(\mathfrak{Y}\) -factors (respectively, is a residually \(\mathfrak{Y}\) -group) if G possesses an invariant system with \(\mathfrak{X}\) - and \(\mathfrak{Y}\) -factors (respectively, is a residually \(\mathfrak{Y}\) -group) and N ∈ \(\mathfrak{X}\) (respectively, N is a maximal invariant \(\mathfrak{X}\) -subgroup of the group G).
Published
25.08.2000
How to Cite
TrebenkoD. Y., and ChernikovN. S. “Quotient Groups of Groups of Certain Classes”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 52, no. 8, Aug. 2000, pp. 1141-3, https://umj.imath.kiev.ua/index.php/umj/article/view/4519.
Section
Short communications