Abelian subgroups of pro-p Galois groups
It is proved that non-trivial normal abelian subgroups of the Galois group of the maximal Galois p-extension of a field F (where p is an odd prime) arise from p-henselian valuations with non-p-divisible value group, provided #(F/FP) p2 and F contains a primitive p-th root of unity. Also, a generaliz...
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| Format: | Journal article |
| Language: | English |
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1998
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| _version_ | 1797067656259436544 |
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| author | Engler, A Koenigsmann, J |
| author_facet | Engler, A Koenigsmann, J |
| author_sort | Engler, A |
| collection | OXFORD |
| description | It is proved that non-trivial normal abelian subgroups of the Galois group of the maximal Galois p-extension of a field F (where p is an odd prime) arise from p-henselian valuations with non-p-divisible value group, provided #(F/FP) p2 and F contains a primitive p-th root of unity. Also, a generalization to arbitrary prime-closed Galois-extensions is given. ©1998 American Mathematical Society. |
| first_indexed | 2024-03-06T21:59:29Z |
| format | Journal article |
| id | oxford-uuid:4e17bd74-49d5-4e40-b524-026c49b8b738 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:59:29Z |
| publishDate | 1998 |
| record_format | dspace |
| spelling | oxford-uuid:4e17bd74-49d5-4e40-b524-026c49b8b7382022-03-26T15:59:10ZAbelian subgroups of pro-p Galois groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4e17bd74-49d5-4e40-b524-026c49b8b738EnglishSymplectic Elements at Oxford1998Engler, AKoenigsmann, JIt is proved that non-trivial normal abelian subgroups of the Galois group of the maximal Galois p-extension of a field F (where p is an odd prime) arise from p-henselian valuations with non-p-divisible value group, provided #(F/FP) p2 and F contains a primitive p-th root of unity. Also, a generalization to arbitrary prime-closed Galois-extensions is given. ©1998 American Mathematical Society. |
| spellingShingle | Engler, A Koenigsmann, J Abelian subgroups of pro-p Galois groups |
| title | Abelian subgroups of pro-p Galois groups |
| title_full | Abelian subgroups of pro-p Galois groups |
| title_fullStr | Abelian subgroups of pro-p Galois groups |
| title_full_unstemmed | Abelian subgroups of pro-p Galois groups |
| title_short | Abelian subgroups of pro-p Galois groups |
| title_sort | abelian subgroups of pro p galois groups |
| work_keys_str_mv | AT englera abeliansubgroupsofpropgaloisgroups AT koenigsmannj abeliansubgroupsofpropgaloisgroups |