Calculs d'invariants primitifs de groupes finis

Free access article

Issue		RAIRO-Theor. Inf. Appl. Volume 33, Number 1, January-February 1999


Page(s)		59 - 77
DOI		10.1051/ita:1999106

DOI: 10.1051/ita:1999106

ITA, Vol. 33, N $^{\rm o}$ 1, 1999, p. 59-77

Calculs d'invariants primitifs de groupes finis

Ines Abdeljaouad
CalFor - LIP6, Université Paris VI, 4 place Jussieu, 75252 Paris Cedex 05, France; (Ines.Abdeljaouad@lip6.fr)

Received September, 1997. Accepted November, 1998.

Abstract: We introduce in this article a new method to calculate all absolute and relatif primitive invariants of finite groups. This method is inspired from K. Girstmair which calculate an absolute primitive invariant of minimal degree. Are presented two algorithms, the first one enable us to calculate all primitive invariants of minimal degree, and the second one calculate all absolute or relative primitive invariants with distincts coefficients. This work take place in Galois Theory and Invariant Theory.

Résumé: Nous introduisons dans cet article un nouvel outil de calcul de tous les invariants primitifs relatifs et absolus de groupes finis. Cette méthode est inspirée par l'algorithme de K. Girstmair qui calcule un invariant primitif absolu de degré minimal. Sont présentés deux algorithmes : le premier algorithme calcule tous les invariants primitifs de degré minimal et le deuxième algorithme calcule tous les invariants primitifs à coefficients distincts. Ce travail entre dans le cadre de la théorie de Galois et la théorie des Invariants.

Communicated by: Ch. Choffrut.

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