On the Nilpotent Multipliers of a Free Product with Topological Approach

Details On the Nilpotent Multipliers of a Free Product with Topological Approach On the Nilpotent Multipliers of a Free Product with Topological Approach

2010-10-02

arxiv.org/abs/1010.0291v2

Mathematics

Algebraic Topology

13 pages

Scientific paper

In this paper, using the topological interpretation of the Baer invariant of a group $G$, $\mathcal{V}M(G)$, with respect to an arbitrary variety $\mathcal{V}$, we extend a result of Burns and Ellis (Math. Z. 226 (1997) 405-428) on second nilpotent multipliers of a free product of two groups to the $c$-nilpotent multipliers for all $c\geq 1$. In particular, we show that $M^{(c)}(G\ast H)\cong M^{(c)}(G)\oplus M^{(c)}(H)$ when $G$ and $H$ are finite groups with some conditions or when $G$ and $H$ are two perfect groups.

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