  We study the Fadell-Husseini index of the configuration space F(R^d,n) with
respect to different subgroups of the symmetric group S_n. For p prime and d>0,
we completely determine Index_{Z/p}(F(R^d,p);F_p) and partially describe
Index{(Z/p)^k}(F(R^d,p^k);F_p). In this process we obtain results of
independent interest, including:
  (1) an extended equivariant Goresky-MacPherson formula,
  (2) a complete description of the top homology of the partition lattice Pi_p
as an F_p[Z_p]-module, and
  (3) a generalized Dold theorem for elementary abelian groups.
  The results on the Fadell-Husseini index yield a new proof of the Nandakumar
& Ramana Rao conjecture for a prime. For n=p^k a prime power, we compute the
Lusternik-Schnirelmann category cat(F(R^d,n)/S_n)=(d-1)(n-1). Moreover, we
extend coincidence results related to the Borsuk-Ulam theorem, as obtained by
Cohen & Connett, Cohen & Lusk, and Karasev & Volovikov.
