On -extensions in characteristic

Author:
Arne Ledet

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2557-2561

MSC (2000):
Primary 12F12; Secondary 12E10, 13B05

DOI:
https://doi.org/10.1090/S0002-9939-04-07394-0

Published electronically:
April 8, 2004

MathSciNet review:
2054780

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the relationship between generic polynomials and generic extensions over a finite ground field, using dihedral extensions as an example.

**[DM]**F. R. DeMeyer,*Generic polynomials*, J. Algebra**84**(1983), 441-448. MR**85a:12007****[D&M]**F. DeMeyer and T. McKenzie,*On generic polynomials*, J. Algebra**261**(2003), 327-333. MR**2003m:12007****[JL&Y]**C. U. Jensen, A. Ledet and N. Yui,*Generic polynomials. Constructive aspects of the inverse Galois problem*, Mathematical Sciences Research Institute Publications, Series 45, Cambridge University Press, Cambridge, 2002. MR**2004d:12007****[Ke]**G. Kemper,*Generic polynomials are descent-generic*, Manuscripta Math.**105**(2001), 139-141. MR**2002k:12009****[Ku]**W. Kuyk,*On a theorem of E. Noether*, Nederl. Akad. Wetensch. Proc. Ser. A**67**= Indag. Math.**26**(1964), 32-39. MR**28:3989****[Le]**A. Ledet,*On -groups in characteristic*, in Algebra, Arithmetic and Geometry with Applications (Christensen, Sundaram, Sathaye, and Bajaj, eds.), Springer-Verlag, 2004, pp. 591-600.**[Noe]**E. Noether,*Gleichungen mit vorgeschriebener Gruppe*, Math. Ann.**78**(1916), 221-229.**[Sa]**D. J. Saltman,*Generic Galois extensions and problems in field theory*, Adv. Math.**43**(1982), 250-283. MR**84a:13007****[Sm]**G. W. Smith,*Generic cyclic polynomials of odd degree*, Comm. Algebra**19**(12) (1991), 3367-3391. MR**93d:12004**

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Additional Information

**Arne Ledet**

Affiliation:
Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409–1042

Email:
aledet@math.ttu.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07394-0

Received by editor(s):
April 23, 2003

Received by editor(s) in revised form:
June 2, 2003

Published electronically:
April 8, 2004

Communicated by:
Lance W. Small

Article copyright:
© Copyright 2004
American Mathematical Society