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 the second nilpotent multiplier 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.}
کلید واژگان :
Baer invariant, Variety of groups, Nilpotent multiplier, Simplicial groups, Direct limit, Perfect group
