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2021 Eisenstein polynomials defining Galois dihedral p -adic fields of degree 2 p
Chad Awtrey, Nicholas Hadgis, Annalise Von Sprecken
Involve 14(3): 463-474 (2021). DOI: 10.2140/involve.2021.14.463

Abstract

Let p > 2 be prime, p the field of p -adic numbers, and f ( x ) p [ x ] an Eisenstein polynomial of degree 2 p . We give necessary and sufficient conditions on the coefficients of f ( x ) for its Galois group to be isomorphic to the dihedral group of order 2 p .

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Chad Awtrey. Nicholas Hadgis. Annalise Von Sprecken. "Eisenstein polynomials defining Galois dihedral p -adic fields of degree 2 p ." Involve 14 (3) 463 - 474, 2021. https://doi.org/10.2140/involve.2021.14.463

Information

Received: 20 September 2020; Accepted: 12 February 2021; Published: 2021
First available in Project Euclid: 30 July 2021

Digital Object Identifier: 10.2140/involve.2021.14.463

Subjects:
Primary: 11S05 , 11S15 , 11S20

Keywords: dihedral , Eisenstein polynomials , p -adic fields , totally ramified extensions

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.14 • No. 3 • 2021
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