For the cyclotomic ℤ2-extension k∞ of an imaginary quadratic field k, we consider whether the Galois group G(k∞) of the maximal unramified pro-2-extension over k∞ is abelian or not. The group G(k∞) is abelian if and only if the nth layer of the ℤ2-extension has abelian 2-class field tower for all n ≥ 1. The purpose of this paper is to classify all such imaginary quadratic fields k in part by using Iwasawa polynomials.
ASJC Scopus subject areas
- 数学 (全般)