Homayoon Arabyani - Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran; Tel.: +۱۲۳-۴۵-۶۷۸۹۱۰ Fax: +۱۲۳-۴۵-۶۷۸۹۱۰

Let V be a variety of groups defined by a set v of laws .Let (N,G) be a pair of groups in which N is a normal subgroup of G. we define the lower and upper V-marginal series of the pair (N,G) and prove some results on the varieties nilpotent pais of groups. Moreover, we extend some properties of the Baer-invariant and isologism of a pairs of groups.

Pair of groups, Baer-invariant, Isologism