Group extensions and marginal series of pair of groups

Abstract

In this article, using the concept of generalized Baer-invariant of a pair of groups, we establish some related isomorphisms between lower marginal quotient pairs of groups, which are generalized versions of some isomorphisms of Stallings. We also derive a result for the pair (V .W , X ) to be an ultra Hall pair for special varieties of groups. This result generalizes that of Fung in 1977, which has roots in Philip Hall's criterion on nilpotency.