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

Frank Gerth III

Acta Arithmetica (1991)

  • Volume: 60, Issue: 1, page 85-92
  • ISSN: 0065-1036

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Frank Gerth III. "On p-class groups of cyclic extensions of prime degree p of number fields." Acta Arithmetica 60.1 (1991): 85-92. <http://eudml.org/doc/206426>.

@article{FrankGerthIII1991,
author = {Frank Gerth III},
journal = {Acta Arithmetica},
keywords = {p-class group; minimal number of generators; relative discriminant; cyclic extensions},
language = {eng},
number = {1},
pages = {85-92},
title = {On p-class groups of cyclic extensions of prime degree p of number fields},
url = {http://eudml.org/doc/206426},
volume = {60},
year = {1991},
}

TY - JOUR
AU - Frank Gerth III
TI - On p-class groups of cyclic extensions of prime degree p of number fields
JO - Acta Arithmetica
PY - 1991
VL - 60
IS - 1
SP - 85
EP - 92
LA - eng
KW - p-class group; minimal number of generators; relative discriminant; cyclic extensions
UR - http://eudml.org/doc/206426
ER -

References

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  1. [1] E. Artin and J. Tate, Class Field Theory, Benjamin, New York 1967. Zbl1179.11040
  2. [2] J. Cassels and A. Fröhlich, Algebraic Number Theory, Thompson, Washington, D.C., 1967. 
  3. [3] Y. Furuta, The genus field and genus number in algebraic number fields, Nagoya Math. J. 29 (1967), 281-285. Zbl0166.05901
  4. [4] F. Gerth, Limit probabilities for coranks of matrices over GF(q), Linear and Multilinear Algebra 19 (1986), 79-93. Zbl0609.15006
  5. [5] F. Gerth, Densities for ranks of certain parts of p-class groups, Proc. Amer. Math. Soc. 99 (1987), 1-8. Zbl0625.12005
  6. [6] F. Gerth, Densities for 3-class ranks in certain cubic extensions, J. Reine Angew. Math. 381 (1987), 161-180. Zbl0622.12008
  7. [7] F. Gerth, On p-class groups of cyclic extensions of prime degree p of quadratic fields, Mathematika 36 (1989), 89-102. Zbl0689.12007
  8. [8] F. Gerth, On p-class groups of cyclic extension of prime degree p of certain cyclotomic fields, Manuscripta Math. 70 (1990), 39-50. Zbl0716.11053

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