Equivariant Iwasawa theory: an example

The equivariant `main conjecture’ of Iwasawa theory is shown to hold for a Galois extension $K\mathrm{/}k$ of number fields with Galois group an $l$-adic pro-$l$ Lie group of dimension 1 containing an abelian subgroup of index $l$, provided that Iwasawa’s $\mu$-invariant $\mu (K\mathrm{/}k)$ vanishes.