  Let G be a Poincare duality group of dimension n. For a given element g in G,
let C_g denote its centralizer subgroup. Let L_G be the graded abelian group
defined by (L_G)_p = oplus_{[g]}H_{p+n}(C_g) where the sum is taken over
conjugacy classes of elements in G. In this paper we construct a multiplication
on L_G directly in terms of intersection products on the centralizers. This
multiplication makes L_G a graded, associative, commutative algebra. When G is
the fundamental group of an aspherical, closed oriented n manifold M, then
(L_G)_* = H_{*+n}(LM), where LM is the free loop space of M. We show that the
product on L_G corresponds to the string topology loop product on H_*(LM)
defined by Chas and Sullivan.
