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Eisenstein
polynomials defining Galois dihedral $p$-adic fields of
degree $2p$
Chad Awtrey, Nicholas Hadgis and Annalise Von Sprecken
Vol. 14 (2021), No. 3, 463–474
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Abstract |
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Let be prime, the field of -adic numbers, and an Eisenstein polynomial of degree . We give necessary and sufficient conditions on the coefficients of for its Galois group to be isomorphic to the dihedral group of order . |
Keywords
Eisenstein polynomials, $p$-adic fields, dihedral, totally
ramified extensions
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Mathematical Subject Classification
Primary: 11S05, 11S15, 11S20
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Milestones
Received: 20 September 2020
Revised: 2 February 2021
Accepted: 12 February 2021
Published: 17 July 2021
Communicated by Kenneth S. Berenhaut
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Authors |
| Chad Awtrey | |
| Department of Mathematics and
Computer Science Samford University Homewood, AL United States |
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| Nicholas Hadgis | |
| Department of Physical Therapy Duke University School of Medicine Durham, NC United States |
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| Annalise Von Sprecken | |
| Department of Mathematics and
Statistics Elon University Elon, NC United States |
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