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| Titel: |
Composita of sextic fields, theory and examples |
| Auteur: |
Roberts, David P. |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 24 (1996) nr. 10 pagina's 3311-3333 |
| Jaar: |
1996 |
| Inhoud: |
Fix a ground field F. Let [image omitted] be a finite collection of finite degree separable field extensions of F. To study how the fields in К are related to each other, one should construct a joint splitting field FК and describe the Galois group Gal(FК/F) In this paper we describe the general appearance of Gal(FК/F) for arbi-trary F when the Fi all have degree ≤ 6. Then we apply this description to three interesting related examples. First and second, we take ground fields the p-adic fields Q2 and Q3, and К the collection of all degree ≤ 6 fields. Third, we take ground field the rational number field Q and К the collection of all degree ≤ 6 fields with absolute discriminant of the form 2a3b This paper complements three of our previous papers. The paper [4] roughly speaking considers the Galois theory associated to a single field K of degree ≤ 6, whereas here we consider a finite collection of such K. The paper [5] lists all degree ≤ 6 fields over Q2 and Q3 . These tables form the basis of our local examples. The paper [2] lists all degree ≤ 6 fields over Q with absolute discriminant of the form 2 3 . These tables form the basis of our global examples. While as indicated we will be making fundamental reference to these three papers, the present paper is nonetheless reasonably self-contained. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 7 van 23 gevonden artikelen
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