Prime decomposition and the Iwasawa MU-invariant

For Gamma = Z(p), Iwasawa was the first to construct Gamma-extensions over number fields with arbitrarily large mu-invariants. In this work, we investigate other uniform pro-p groups which are realisable as Galois groups of towers of number fields with arbitrarily large mu-invariant. For instance, we prove that this is the case if p is a regular prime and Gamma is a uniform prop group admitting a fixed-point-free automorphism of odd order dividing p - 1. Both in Iwasawa's work, and in the present one, the size of the mu-invariant appears to be intimately related to the existence of primes that split completely in the tower.