Abstract
Let p be an odd prime number, K an imaginary abelian field with ζ p ∈ K × , and K ∞ / K the cyclotomic Z p -extension with its n th layer K n . In the previous paper, we showed that for any n and any unramified cyclic extension L / K n of degree p , LK n +1 / K n +1 does have a normal integral basis (NIB) even if L / K n 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 .
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