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...
Збережено в:
| Дата: | 2009 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2009
|
| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154610 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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| id |
irk-123456789-154610 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1546102019-06-16T01:28:12Z On Galois groups of prime degree polynomials with complex roots Oz Ben-Shimol 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. 2009 Article 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 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Oz Ben-Shimol |
| spellingShingle |
Oz Ben-Shimol On Galois groups of prime degree polynomials with complex roots Algebra and Discrete Mathematics |
| author_facet |
Oz Ben-Shimol |
| author_sort |
Oz Ben-Shimol |
| title |
On Galois groups of prime degree polynomials with complex roots |
| title_short |
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_sort |
on galois groups of prime degree polynomials with complex roots |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154610 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT ozbenshimol ongaloisgroupsofprimedegreepolynomialswithcomplexroots |
| first_indexed |
2023-05-20T17:44:27Z |
| last_indexed |
2023-05-20T17:44:27Z |
| _version_ |
1796153980772941824 |