Proceedings of the Japan Academy, Series A, Mathematical Sciences

The number of modular extensions of odd degree of a local field

Masakazu Yamagishi

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Abstract

The number of Galois extensions, up to isomorphism, of a local field whose Galois groups are isomorphic to the modular group $M_{p^{m}}=\langle x,y\mid x^{p^{m-1}}=y^{p}=1,y^{-1}xy=x^{p^{m-2}+1}\rangle$, where $p$ is an odd prime, is counted.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 84, Number 8 (2008), 151-153.

Dates
First available in Project Euclid: 6 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.pja/1223299524

Digital Object Identifier
doi:10.3792/pjaa.84.151

Mathematical Reviews number (MathSciNet)
MR2457804

Zentralblatt MATH identifier
1225.11154

Subjects
Primary: 11S20: Galois theory

Keywords
Local field $p$-extension

Citation

Yamagishi, Masakazu. The number of modular extensions of odd degree of a local field. Proc. Japan Acad. Ser. A Math. Sci. 84 (2008), no. 8, 151--153. doi:10.3792/pjaa.84.151. https://projecteuclid.org/euclid.pja/1223299524


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References

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