Geodesic
The Normal Closure of a Quadratic Extension of a Cyclic Quartic Field
Canadian journal of mathematics, Tome 43 (1991) no. 5, pp. 1086-1097

Voir la notice de l'article provenant de la source Cambridge University Press

Pierre Barrucand asks the following question (Unsolved Problems, # ASI 88:04, Banff, May 1988, Richard K. Guy, Ed.; also [2, p. 594]). Let K be a cyclic quartic field, and let ξ be a non-square element of K. Let M be the Galois closure of , and let G be the Galois group Gal(M/Q). Find (1) all possible G, (2) conditions on ξ to have such a G, and (3) a list of all possible subfields of M.
DOI : 10.4153/CJM-1991-063-4
Mots-clés : 12F05, quadratic extension, cyclic quartic field 
Vaughan, Theresa P. The Normal Closure of a Quadratic Extension of a Cyclic Quartic Field. Canadian journal of mathematics, Tome 43 (1991) no. 5, pp. 1086-1097. doi: 10.4153/CJM-1991-063-4
@article{10_4153_CJM_1991_063_4,
     author = {Vaughan, Theresa P.},
     title = {The {Normal} {Closure} of a {Quadratic} {Extension} of a {Cyclic} {Quartic} {Field}},
     journal = {Canadian journal of mathematics},
     pages = {1086--1097},
     year = {1991},
     volume = {43},
     number = {5},
     doi = {10.4153/CJM-1991-063-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-063-4/}
}
TY  - JOUR
AU  - Vaughan, Theresa P.
TI  - The Normal Closure of a Quadratic Extension of a Cyclic Quartic Field
JO  - Canadian journal of mathematics
PY  - 1991
SP  - 1086
EP  - 1097
VL  - 43
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-063-4/
DO  - 10.4153/CJM-1991-063-4
ID  - 10_4153_CJM_1991_063_4
ER  - 
%0 Journal Article
%A Vaughan, Theresa P.
%T The Normal Closure of a Quadratic Extension of a Cyclic Quartic Field
%J Canadian journal of mathematics
%D 1991
%P 1086-1097
%V 43
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-063-4/
%R 10.4153/CJM-1991-063-4
%F 10_4153_CJM_1991_063_4

[1] 1. Hall, M., Jr. and Senior, J.K., The groups of order 2n(n ≥6). Macmillan, 1964. Google Scholar

[2] 2. Mollin, R.A., Number Theory and Applications. Kluwer, 1989. Google Scholar

[3] 3. van der Waerden, B.L., Modern Algebra. Frederick Ungar Publishing, New York, 1950. Google Scholar

[4] 4. Thomas, A.D. and Wood, G.V., Group Tables. Shiva Publishing Ltd., Orpington, Kent, UK, 1980. Google Scholar

Cité par Sources :