Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-23T08:29:23.868Z Has data issue: false hasContentIssue false
  • English
  • Français

Explicit Classifications of Some 2-Extensions of a Field of Characteristic Different from 2

Published online by Cambridge University Press:  20 November 2018

Ian Kiming
Ian Kiming*
Affiliation:
Inst. for Experimental Math., Ellernstraβe 29, 4300 Essen, Germany
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let p be a prime number. Let k be a field of characteristic different from p and containing the p-th roots of unity. Let be a finite group. Let L/k be a finite normal extension with Galois group and let c be a 2-cocycle on with coefficients in , where acts trivially on By Emb(L/k, c) we denote the question of the existence of a finite normal extension M of k, such that M contains L, such that [M: L] = p, and such that, denoting by the Galois group of M/k, the extension is given by the class of c.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 5 , 01 October 1990 , pp. 825 - 855
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Damey, P., Martinet, J., Plongement d'une extension quadratique dans une extension quaternionienne, J. reine angew. Math. 262/263 (1974) 323–338.Google Scholar
2. Jensen, C.U., Yui, N., Quaternion Extensions, Algebraic Geormetry and Commutative Algebra in Honour of Masayoshi NAG ATA, Kinokuniya, Tokyo (1987) 155–182.Google Scholar
3. Massy, R., Construction de p-extensions galoisiennes d'un corps de caractéristique différente de p,, J. Algebra 109 (1987) 508–535.Google Scholar
4. Lamprecht, E., Zur Charakterisierung zyklischer Erweiterungen rationaler Funktionenkôrper, II, Arch. Math. (Basel) 13 (1962) 488–497.Google Scholar
5. Witt, E., Konstruktion von galoisschen Körpern der Charakteristik p zu vorgegebener Gruppe der Ordnung pf , J. reine angew. Math. 174(1936) 237–245.Google Scholar