Affiliation:
1. Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran
Abstract
AbstractIn this paper, we use the theory of simplicial groups to generalize the Schur multiplier of a pair of groups {(G,N)} to its Baer invariant, {\mathcal{V}M(G,N)}, with respect to an arbitrary variety {\mathcal{V}}. Moreover, among other things we present some behaviors of Baer invariants of a pair of groups with respect to the free product and the direct limit.
Finally, we prove that the nilpotent multiplier of a pair of groups does commute with the free product of finite groups of mutually coprime orders.
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