On Galois groups of prime degree polynomials with complex roots

Let f be an irreducible polynomial of prime degree p≥5 over Q, with precisely k pairs of complex roots. Using a result of Jens Hochsmann (1999), show that if p≥4k+1 then Gal(f/Q) is isomorphic to Ap or Sp. This improves the algorithm for computing the Galois group of an irreducible polynomial of p...

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Бібліографічні деталі
Опубліковано в: :Algebra and Discrete Mathematics
Дата:2009
Автор: Oz Ben-Shimol
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут прикладної математики і механіки НАН України 2009
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/154610
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:On Galois groups of prime degree polynomials with complex roots / Oz Ben-Shimol // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 2. — С. 99–107. — Бібліогр.: 19 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Oz Ben-Shimol
author_facet Oz Ben-Shimol
citation_txt On Galois groups of prime degree polynomials with complex roots / Oz Ben-Shimol // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 2. — С. 99–107. — Бібліогр.: 19 назв. — англ.
collection DSpace DC
container_title Algebra and Discrete Mathematics
description Let f be an irreducible polynomial of prime degree p≥5 over Q, with precisely k pairs of complex roots. Using a result of Jens Hochsmann (1999), show that if p≥4k+1 then Gal(f/Q) is isomorphic to Ap or Sp. This improves the algorithm for computing the Galois group of an irreducible polynomial of prime degree, introduced by A. Bialostocki and T. Shaska.
 
 If such a polynomial f is solvable by radicals then its Galois group is a Frobenius group of degree p. Conversely, any Frobenius group of degree p and of even order, can be realized as the Galois group of an irreducible polynomial of degree p over Q having complex roots.
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publishDate 2009
publisher Інститут прикладної математики і механіки НАН України
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spelling Oz Ben-Shimol
2019-06-15T16:50:49Z
2019-06-15T16:50:49Z
2009
On Galois groups of prime degree polynomials with complex roots / Oz Ben-Shimol // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 2. — С. 99–107. — Бібліогр.: 19 назв. — англ.
1726-3255
2000 Mathematics Subject Classification:20B35; 12F12.
https://nasplib.isofts.kiev.ua/handle/123456789/154610
Let f be an irreducible polynomial of prime degree p≥5 over Q, with precisely k pairs of complex roots. Using a result of Jens Hochsmann (1999), show that if p≥4k+1 then Gal(f/Q) is isomorphic to Ap or Sp. This improves the algorithm for computing the Galois group of an irreducible polynomial of prime degree, introduced by A. Bialostocki and T. Shaska.
 
 If such a polynomial f is solvable by radicals then its Galois group is a Frobenius group of degree p. Conversely, any Frobenius group of degree p and of even order, can be realized as the Galois group of an irreducible polynomial of degree p over Q having complex roots.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
On Galois groups of prime degree polynomials with complex roots
Article
published earlier
spellingShingle On Galois groups of prime degree polynomials with complex roots
Oz Ben-Shimol
title On Galois groups of prime degree polynomials with complex roots
title_full On Galois groups of prime degree polynomials with complex roots
title_fullStr On Galois groups of prime degree polynomials with complex roots
title_full_unstemmed On Galois groups of prime degree polynomials with complex roots
title_short On Galois groups of prime degree polynomials with complex roots
title_sort on galois groups of prime degree polynomials with complex roots
url https://nasplib.isofts.kiev.ua/handle/123456789/154610
work_keys_str_mv AT ozbenshimol ongaloisgroupsofprimedegreepolynomialswithcomplexroots