Polynomials whose Galois groups are Frobenius groups with prime order complement

Cangelmi, Leonardo

Cangelmi, Leonardo

Journal de théorie des nombres de Bordeaux, Tome 6 (1994) no. 2, pp. 391-406.

Résumé
Abstract

On donne une caractérisation effective des polynômes irréductibles de degré $n$ à coefficients entiers dont les groupes de Galois sur $ℚ$ sont des groupes de Frobenius avec noyau d’ordre $n$ et complément d’ordre premier.

We give an effective characterization theorem for integral monic irreducible polynomials $f$ of degree $n$ whose Galois groups over $ℚ$ are Frobenius groups with kernel of order $n$ and complement of prime order.

MR Zbl

Classification : Primary 12F10, 12Y05, Secondary 12F12, 12-04
Mots-clés : effective characterization of polynomials with given Galois groups, Frobenius groups with prime order complement

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     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://www.numdam.org/item/JTNB_1994__6_2_391_0/}
}

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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://www.numdam.org/item/JTNB_1994__6_2_391_0/

Bibliographie
Cité par

[BJY] A.A. Bruen, C.U. Jensen, N. Yui, Polynomials with Frobenius groups of prime deegre as Galois groups II, J. Number Theory 24 (1986), 305-359. | MR | Zbl

[Frob] G. Frobenius, Über Beziehungen zwischen den Primidealen eines algebraischen Körpers und den Substitution seiner Gruppe, S. B. Akad. Wiss. Berlin (1896), 689-705. | JFM

[Jac] N. Jacobson, Basic algebra I, 2nd ed., Freeman, New York, 1985. | MR | Zbl

[Lang] S. Lang, Algebraic number theory, GTM 110, Springer-Verlag, New York, 1986. | MR | Zbl

[LMO] J.C. Lagarias, H.L. Montgomery, A.M. Odlyzko, A bound for the least prime ideal in the Chebotarev density theorem, Invent. Math. 54 (1979), 271-296. | MR | Zbl

[Oes] J. Oesterlé, Versions effectives du théorème de Chebotarev sous l'hypothèse de Riemann généralisé, Astérisque 61 (1979), 165-167. | Numdam | Zbl

[Rob] D.J.S. Robinson, A course in the theory of groups, GTM 80, Springer-Verlag, New York, 1982. | MR | Zbl

[Trag] B.M. Trager, 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] B. L. Van Der Waerden, Modern algebra, 2nd ed., vol. I, Ungar, New York, 1953. | Zbl

[Will] C.J. Williamson, Odd degree polynomials with dihedral Galois groups, J. Number Theory 34 (1990), 153-173. | MR | Zbl