On Baer Invariants of Pairs of Groups

Details On Baer Invariants of Pairs of Groups On Baer Invariants of Pairs of Groups

2011-06-07

arxiv.org/abs/1106.1278v1

Mathematics

Algebraic Topology

21 pages

Scientific paper

In this paper, we use the theory of simplicial groups to develop the Schur multiplier of a pair of groups $(G,N)$ to the Baer invariant of it, $\mathcal{V}M(G,N)$, with respect to an arbitrary variety $\mathcal{V}$. Moreover, we present among other things 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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