Some Remarks on the Varieties of Pairs of Groups

Document Type : Research Paper


Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran; Tel.: +123-45-678910 Fax: +123-45-678910


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