Polynomials whose Galois groups are Frobenius groups with prime order complement

Leonardo Cangelmi

Journal de théorie des nombres de Bordeaux (1994)

  • Volume: 6, Issue: 2, page 391-406
  • ISSN: 1246-7405

Abstract

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

How to cite

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Cangelmi, Leonardo. "Polynomials whose Galois groups are Frobenius groups with prime order complement." Journal de théorie des nombres de Bordeaux 6.2 (1994): 391-406. <http://eudml.org/doc/93610>.

@article{Cangelmi1994,
abstract = {We give an effective characterization theorem for integral monic irreducible polynomials $f$ of degree $n$ whose Galois groups over $\mathbb \{Q\}$ are Frobenius groups with kernel of order $n$ and complement of prime order.},
author = {Cangelmi, Leonardo},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {effective characterization of polynomials with given Galois groups; Frobenius groups with prime order complement; inverse Galois problem; resultant polynomial; irreducible polynomials; Galois groups; Frobenius groups; complement of prime order},
language = {eng},
number = {2},
pages = {391-406},
publisher = {Université Bordeaux I},
title = {Polynomials whose Galois groups are Frobenius groups with prime order complement},
url = {http://eudml.org/doc/93610},
volume = {6},
year = {1994},
}

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
PB - Université Bordeaux I
VL - 6
IS - 2
SP - 391
EP - 406
AB - We give an effective characterization theorem for integral monic irreducible polynomials $f$ of degree $n$ whose Galois groups over $\mathbb {Q}$ are Frobenius groups with kernel of order $n$ and complement of prime order.
LA - eng
KW - effective characterization of polynomials with given Galois groups; Frobenius groups with prime order complement; inverse Galois problem; resultant polynomial; irreducible polynomials; Galois groups; Frobenius groups; complement of prime order
UR - http://eudml.org/doc/93610
ER -

References

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  1. [BJY] A.A. Bruen, C.U. Jensen, N. Yui, Polynomials with Frobenius groups of prime deegre as Galois groups II, J. Number Theory24 (1986), 305-359. Zbl0598.12009MR866976
  2. [Frob] G. Frobenius, Über Beziehungen zwischen den Primidealen eines algebraischen Körpers und den Substitution seiner Gruppe, S. B. Akad. Wiss. Berlin (1896), 689-705. Zbl27.0091.04JFM27.0091.04
  3. [Jac] N. Jacobson, Basic algebra I, 2nd ed., Freeman, New York, 1985. Zbl0557.16001MR780184
  4. [Lang] S. Lang, Algebraic number theory, GTM 110, Springer-Verlag, New York, 1986. Zbl0601.12001MR1282723
  5. [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. Zbl0401.12014MR553223
  6. [Oes] J. Oesterlé, Versions effectives du théorème de Chebotarev sous l'hypothèse de Riemann généralisé, Astérisque61 (1979), 165-167. Zbl0418.12005
  7. [Rob] D.J.S. Robinson, A course in the theory of groups, GTM 80, Springer-Verlag, New York, 1982. Zbl0483.20001MR648604
  8. [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. Zbl0498.12005
  9. [vdW] B. L. van der Waerden, Modern algebra, 2nd ed., vol. I, Ungar, New York, 1953. Zbl0039.00902
  10. [Will] C.J. Williamson, Odd degree polynomials with dihedral Galois groups, J. Number Theory34 (1990), 153-173. Zbl0814.11054MR1042489

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