Quadratic subfields on quartic extensions of local fields
We show that any quartic extension of a local field of odd residue characteristic must contain an intermediate field. A consequence of this is that local fields of odd residue characteristic do not have extensions with Galois group A4 or S4. Counterexamples are given for even residue characteristic.
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171288000018 |
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| _version_ | 1832567697206935552 |
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| author | Joe Repka |
| author_facet | Joe Repka |
| author_sort | Joe Repka |
| collection | DOAJ |
| description | We show that any quartic extension of a local field of odd residue characteristic must contain an intermediate field. A consequence of this is that local fields of odd residue characteristic do not have extensions with Galois group A4 or S4. Counterexamples are given for even residue characteristic. |
| format | Article |
| id | doaj-art-f6a64ce19b3045f0b849cae3b8b2aa0b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f6a64ce19b3045f0b849cae3b8b2aa0b2025-02-03T01:00:53ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-011111410.1155/S0161171288000018Quadratic subfields on quartic extensions of local fieldsJoe Repka0Mathematics Department, University of Toronto, Ontario, Toronto M5S 1A1, CanadaWe show that any quartic extension of a local field of odd residue characteristic must contain an intermediate field. A consequence of this is that local fields of odd residue characteristic do not have extensions with Galois group A4 or S4. Counterexamples are given for even residue characteristic.http://dx.doi.org/10.1155/S0161171288000018local fieldquartic extensionendoscopic group. |
| spellingShingle | Joe Repka Quadratic subfields on quartic extensions of local fields International Journal of Mathematics and Mathematical Sciences local field quartic extension endoscopic group. |
| title | Quadratic subfields on quartic extensions of local fields |
| title_full | Quadratic subfields on quartic extensions of local fields |
| title_fullStr | Quadratic subfields on quartic extensions of local fields |
| title_full_unstemmed | Quadratic subfields on quartic extensions of local fields |
| title_short | Quadratic subfields on quartic extensions of local fields |
| title_sort | quadratic subfields on quartic extensions of local fields |
| topic | local field quartic extension endoscopic group. |
| url | http://dx.doi.org/10.1155/S0161171288000018 |
| work_keys_str_mv | AT joerepka quadraticsubfieldsonquarticextensionsoflocalfields |