Let be positive square-free integers, and . Let be the Hilbert -class field of , be the Hilbert -class field of and be the Galois group of . Our goal is to show that there is some form of such is a nonmetacyclic -group and give the necessary condition and sufficient for the group to be metacyclic in case with a prime number such that .
Soient est un entier sans facteurs carrés, , , le -corps de classes de Hilbert de , le -corps de classes de Hilbert de et le groupe de Galois de . Notre but est de montrer qu’il existe une forme de tel que le -groupe est non métacyclique et de donner une condition nécessaire et suffisante pour que le groupe soit métacyclique dans le cas où avec un nombre premier tel que .
@article{AMBP_2009__16_1_83_0, author = {Abdelmalek Azizi and Mohammed Taous}, title = {Condition n\'ecessaire et suffisante pour que certain groupe de {Galois} soit m\'etacyclique}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {83--92}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {16}, number = {1}, year = {2009}, doi = {10.5802/ambp.255}, mrnumber = {2514529}, zbl = {1168.11046}, language = {fr}, url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.255/} }
TY - JOUR AU - Abdelmalek Azizi AU - Mohammed Taous TI - Condition nécessaire et suffisante pour que certain groupe de Galois soit métacyclique JO - Annales mathématiques Blaise Pascal PY - 2009 SP - 83 EP - 92 VL - 16 IS - 1 PB - Annales mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.255/ DO - 10.5802/ambp.255 LA - fr ID - AMBP_2009__16_1_83_0 ER -
%0 Journal Article %A Abdelmalek Azizi %A Mohammed Taous %T Condition nécessaire et suffisante pour que certain groupe de Galois soit métacyclique %J Annales mathématiques Blaise Pascal %D 2009 %P 83-92 %V 16 %N 1 %I Annales mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.255/ %R 10.5802/ambp.255 %G fr %F AMBP_2009__16_1_83_0
Abdelmalek Azizi; Mohammed Taous. Condition nécessaire et suffisante pour que certain groupe de Galois soit métacyclique. Annales mathématiques Blaise Pascal, Volume 16 (2009) no. 1, pp. 83-92. doi : 10.5802/ambp.255. https://ambp.centre-mersenne.org/articles/10.5802/ambp.255/
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