Abstract
Let K / k K/k be a Galois extension of finite degree, and let K ′ K’ denote the maximal abelian extension over k k contained in the Hilbert class field of K K . We give formulas about the group structure of G a l ( K ′ / k ) Gal(K’/k) and the genus group of K / k K/k , which refine the ordinary genus formula.
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