Prime Decomposition and the Iwasawa mu-invariant

For $Γ=\mathbb{Z}_p$, Iwasawa was the first to construct $Γ$-extensions over number fields with arbitrarily large $μ$-invariants. In this work, we investigate other uniform pro-$p$ groups which are realizable as Galois groups of towers of number fields with arbitrarily large $μ$-invariant. For instance, we prove that this is the case if $p$ is a regular prime and $Γ$ is a uniform pro-$p$ 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 $μ$-invariant appears to be intimately related to the existence of primes that split completely in the tower.

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