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

Acta Arithmetica (1991)

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

## Access Full Article

top## How to cite

topFrank 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

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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.