Abstract
For an algebraic number field [Formula: see text] and a prime number [Formula: see text], let [Formula: see text] be the maximal multiple [Formula: see text]-extension. Greenberg’s generalized conjecture (GGC) predicts that the Galois group of the maximal unramified abelian pro-[Formula: see text] extension of [Formula: see text] is pseudo-null over the completed group ring [Formula: see text]. We show that GGC holds for some imaginary quartic fields containing imaginary quadratic fields and some prime numbers.
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