An Equivariant Version of an Index Formula of Fröhlich and McCulloh Original Research Article

By Iwasawaʹs index formula, the order of the minus class groupCl(image[ζp])−equals the index ofI−in imageG−, whereG=Gal(image(ζp)/image) andIis the Stickelberger ideal in imageG. Fröhlich and McCulloh proved a very similar theorem concerning the order ofCl[imageΓ]−, whereΓis any finite elementary abelian group. The proof uses Iwasawaʹs formula. We show how the Main Conjecture of Iwasawa theory implies aG-invariant strengthening of Iwasawaʹs formula. This allows us to prove the main result of this note: a sharpened equivariant version of the above-mentioned result of Fröhlich and McCulloh.