Group extensions and marginal series of pair of groups - Rismanchian, Mohammad Reza (Comptes Rendus. Mathématique, 2021)
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 $(\mathcal{V}.\mathcal{W}, \mathcal{X})$ 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.