Toward equivariant Iwasawa theory, IV

Let l be an odd prime number and K-infinity/k a Galois extension of totally real number fields, with k/Q and K-infinity/k(infinity) finite, where k(infinity) is the cyclotomic Z(l)-extension of k. In [RW2] a "main conjecture" of equivariant Iwasawa theory is formulated which for pro-l groups G(infinity) is reduced in [RW3] to a property of the Iwasawa L-function of K-infinity/k. In this paper we extend this reduction for arbitrary G(infinity) to l-elementary groups G(infinity) = < s > x U, with h < s > a finite cyclic group of order prime to l and U a pro-l group. We also give first nonabelian examples of groups G(infinity) for which the conjecture holds.