Some Results on Isologism of Pairs of Groups

Let ν be a variety of groups defined by a set V of laws. Then the verbal subgroup and the marginal subgroup of a group G associated with the variety are denoted by V (G) and V∗(G), respectively. Let (N, G) be a pair of groups in which N is a normal subgroup of G. In the paper, we study the lower and upper ν-marginal series of the pair (N, G) and prove some properties of isologism of pairs of groups.