Abstract :
Let p be an odd prime number, K an imaginary abelian field with ζpset membership, variantK×, and K∞/K the cyclotomic Zp-extension with its nth layer Kn. In the previous paper, we showed that for any n and any unramified cyclic extension L/Kn of degree p, LKn+1/Kn+1 does have a normal integral basis (NIB) even if L/Kn has no NIB, under the assumption that p does not divide the class number of the maximal real subfield K+ (and some additional assumptions on K). In this paper, we show that similar but more delicate phenomena occur for a certain class of tamely ramified extensions of degree p.
