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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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2009 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154610 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862607278629191680 |
|---|---|
| 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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| first_indexed | 2025-11-28T14:05:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154610 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-28T14:05:13Z |
| publishDate | 2009 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| 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 |