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- W2838592238 abstract "Let $k$ be an imaginary quadratic field with $operatorname{Cl}_{2}(k)simeq V_{4}$ . It is known that the length of the Hilbert $2$ -class field tower is at least $2$ . Gerth ( On 2-class field towers for quadratic number fields with $2$ - class group of type $(2,2)$ , Glasgow Math. J. 40 (1) (1998), 63–69) calculated the density of $k$ where the length of the tower is $1$ ; that is, the maximal unramified $2$ -extension is a $V_{4}$ -extension. In this paper, we shall extend this result for generalized quaternion, dihedral, and semidihedral extensions of small degrees." @default.
- W2838592238 created "2018-07-19" @default.
- W2838592238 creator A5017753579 @default.
- W2838592238 date "2018-07-09" @default.
- W2838592238 modified "2023-09-25" @default.
- W2838592238 title "DISTRIBUTION OF GALOIS GROUPS OF MAXIMAL UNRAMIFIED 2-EXTENSIONS OVER IMAGINARY QUADRATIC FIELDS" @default.
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- W2838592238 doi "https://doi.org/10.1017/nmj.2018.16" @default.
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