Stickelberger ideals of conductor p and their application

Let p be an odd prime number and F a number field. Let K = F(zeta(p)) and Delta = Gal(K/F). Let L-Delta be the Stickelberger ideal of the group ring Z [Delta] defined in the previous paper [8]. As a consequence of a p-integer version of a theorem of McCulloh [15], [16], it follows that F has the Hilbert-Speiser type property for the rings of p-integers of elementary abelian extensions over F of exponent p if and only if the ideal L-Delta annihilates the p-ideal class group of K. In this paper, we study some properties of the ideal L-Delta, and check whether or not a subfield of Q(zeta(p)) satisfies the above property.