On p-class groups of cyclic extensions of prime degree p of number fields

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Department of Mathematics, the University of Texas at Austin, Austin, Texas 78712, U.S.A.

E. Artin and J. Tate, Class Field Theory, Benjamin, New York 1967.
J. Cassels and A. Fröhlich, Algebraic Number Theory, Thompson, Washington, D.C., 1967.
Y. Furuta, The genus field and genus number in algebraic number fields, Nagoya Math. J. 29 (1967), 281-285.
F. Gerth, Limit probabilities for coranks of matrices over GF(q), Linear and Multilinear Algebra 19 (1986), 79-93.
F. Gerth, Densities for ranks of certain parts of p-class groups, Proc. Amer. Math. Soc. 99 (1987), 1-8.
F. Gerth, Densities for 3-class ranks in certain cubic extensions, J. Reine Angew. Math. 381 (1987), 161-180.
F. Gerth, On p-class groups of cyclic extensions of prime degree p of quadratic fields, Mathematika 36 (1989), 89-102.
F. Gerth, On p-class groups of cyclic extension of prime degree p of certain cyclotomic fields, Manuscripta Math. 70 (1990), 39-50.