On donne une caractérisation effective des polynômes irréductibles de degré à coefficients entiers dont les groupes de Galois sur sont des groupes de Frobenius avec noyau d’ordre et complément d’ordre premier.
We give an effective characterization theorem for integral monic irreducible polynomials of degree whose Galois groups over are Frobenius groups with kernel of order and complement of prime order.
Mots-clés : effective characterization of polynomials with given Galois groups, Frobenius groups with prime order complement
@article{JTNB_1994__6_2_391_0, author = {Cangelmi, Leonardo}, title = {Polynomials whose {Galois} groups are {Frobenius} groups with prime order complement}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {391--406}, publisher = {Universit\'e Bordeaux I}, volume = {6}, number = {2}, year = {1994}, mrnumber = {1360652}, zbl = {0828.12004}, language = {en}, url = {http://archive.numdam.org/item/JTNB_1994__6_2_391_0/} }
TY - JOUR AU - Cangelmi, Leonardo TI - Polynomials whose Galois groups are Frobenius groups with prime order complement JO - Journal de théorie des nombres de Bordeaux PY - 1994 SP - 391 EP - 406 VL - 6 IS - 2 PB - Université Bordeaux I UR - http://archive.numdam.org/item/JTNB_1994__6_2_391_0/ LA - en ID - JTNB_1994__6_2_391_0 ER -
%0 Journal Article %A Cangelmi, Leonardo %T Polynomials whose Galois groups are Frobenius groups with prime order complement %J Journal de théorie des nombres de Bordeaux %D 1994 %P 391-406 %V 6 %N 2 %I Université Bordeaux I %U http://archive.numdam.org/item/JTNB_1994__6_2_391_0/ %G en %F JTNB_1994__6_2_391_0
Cangelmi, Leonardo. Polynomials whose Galois groups are Frobenius groups with prime order complement. Journal de théorie des nombres de Bordeaux, Tome 6 (1994) no. 2, pp. 391-406. http://archive.numdam.org/item/JTNB_1994__6_2_391_0/
[BJY] Polynomials with Frobenius groups of prime deegre as Galois groups II, J. Number Theory 24 (1986), 305-359. | MR | Zbl
, , ,[Frob] Über Beziehungen zwischen den Primidealen eines algebraischen Körpers und den Substitution seiner Gruppe, S. B. Akad. Wiss. Berlin (1896), 689-705. | JFM
,[Jac] Basic algebra I, 2nd ed., Freeman, New York, 1985. | MR | Zbl
,[Lang] Algebraic number theory, GTM 110, Springer-Verlag, New York, 1986. | MR | Zbl
,[LMO] A bound for the least prime ideal in the Chebotarev density theorem, Invent. Math. 54 (1979), 271-296. | MR | Zbl
, , ,[Oes] Versions effectives du théorème de Chebotarev sous l'hypothèse de Riemann généralisé, Astérisque 61 (1979), 165-167. | Numdam | Zbl
,[Rob] A course in the theory of groups, GTM 80, Springer-Verlag, New York, 1982. | MR | Zbl
,[Trag] Algebraic factoring and rational function integration, ACM Symposium on Symbolic and Algebraic Computation 1976 (Jenks, ed.), ACM Inc., New York, 1976, pp. 219-226. | Zbl
,[vdW] Modern algebra, 2nd ed., vol. I, Ungar, New York, 1953. | Zbl
,[Will] Odd degree polynomials with dihedral Galois groups, J. Number Theory 34 (1990), 153-173. | MR | Zbl
,