On Galois groups of prime degree polynomials with complex roots
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On Galois groups of prime degree polynomials with complex roots
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| Creator |
Oz Ben-Shimol
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| 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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| Date |
2019-06-15T16:50:49Z
2019-06-15T16:50:49Z 2009 |
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| Type |
Article
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| Identifier |
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. http://dspace.nbuv.gov.ua/handle/123456789/154610 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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