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 nth 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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