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Showing papers on "Generic polynomial published in 1990"



Journal ArticleDOI
TL;DR: In this paper, it was shown that F(G) can be expressed as a kind of a-twisted invariant field when G is a nonsplit extension of G. The goal of this paper is to present this fact and then draw a series of conclusions using it.

17 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that A5 is K-admissible for any number field K such that H is any subgroup of SL(2, 5) which contains a S2-group.
Abstract: Let K be a field and let G be a finite group. G is K-admissible if there exists a Galois extension L of K with G=Gal(L/K) such that L is a maximal subfield of a central K-division algebra. We characterize those number fields K such that H is K-admissible where H is any subgroup of SL(2, 5) which contains a S2-group. The method also yields refinements and alternate proofs of some known results including the fact that A5 is K-admissible for every number field K.

14 citations


Journal ArticleDOI
TL;DR: The existence of permutation polynomials of even degree was proved in this paper, where it was shown that a polynomial F ove q of thr Fe form F r, = wher L e L is an affine lin-earized polynome over F, such that / = g(F) for some poynomial g q>r and the part ofwhich splits completely into linear factors over the algebraic closur q ie osf exactl ¥
Abstract: For a polynomial f(x) over a finite field q , denote F the polynomial f{y)-f(x) by f(x,y).The polynomial ipj has frequently been used in questions on the values of /. The existenceis proved here of a polynomial F ove q of thr Fe form F r , = wher L e L is an affine lin-earized polynomial over F , such that / = g(F) for some polynomial g q>r and the part ofwhich splits completely into linear factors over the algebraic closur q ie osf exactl ¥

13 citations


Journal ArticleDOI
TL;DR: In this article, the authors construct a small category whose objects are monic square-free polynomials with coefficients in a field F, and prove that for a monic, irreducible, and normal polynomial, Aut ( f ) is the usual Galois group of f.

2 citations