Some Structural Properties of Upper and Lower Central Series of Pairs of Groups

Document Type : Original Scientific Paper


Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran


In this paper‎, ‎we first present some properties of lower and upper central series of pair of groups‎. ‎Then the notion of n-isoclinism for the classification of pairs of groups is introduced‎, ‎and some of the structural properties of the created classes are proved‎. ‎Moreover some interesting theorems such as Baer Theorem‎, ‎Bioch Theorem‎, ‎Hirsh Theorem for pair of groups are generalized‎. ‎Finally‎, ‎it is shown that each n-isoclinism family of pairs contains a quotient irreducible pair‎.


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