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Degree 14 2-adic
fields
Chad Awtrey, Nicole Miles, Jonathan Milstead, Christopher Shill and Erin Strosnider
Vol. 8 (2015), No. 2, 329–336
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Abstract |
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We study the 590 nonisomorphic degree 14 extensions of the 2-adic numbers by computing defining polynomials for each extension as well as basic invariant data for each polynomial, including the ramification index, residue degree, discriminant exponent, and Galois group. Our study of the Galois groups of these extensions shows that only 10 of the 63 transitive subgroups of occur as a Galois group. We end by describing our implementation for computing Galois groups in this setting, which is of interest since it uses subfield information, the discriminant, and only one other resolvent polynomial. |
Keywords
2-adic, extension fields, Galois group, local field
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Mathematical Subject Classification 2010
Primary: 11S15, 11S20
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Milestones
Received: 11 August 2013
Revised: 28 August 2013
Accepted: 29 August 2013
Published: 3 March 2015
Communicated by Nigel Boston
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Authors |
| Chad Awtrey | |
| Department of Mathematics and
Statistics Elon University Campus Box 2320 Elon, NC 27244 United States |
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| Nicole Miles | |
| Department of Mathematics and
Statistics Elon University Campus Box 3753 Elon, NC 27244 United States |
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| Jonathan Milstead | |
| Department of Mathematics and
Statistics University of North Carolina 116 Petty Building 317 College Ave Greensboro, NC 27412 United States |
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| Christopher Shill | |
| Department of Mathematics and
Statistics Elon University Campus Box 9017 Elon, NC 27244 United States |
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| Erin Strosnider | |
| Department of Mathematics and
Statistics Elon University Campus Box 5470 Elon, NC 27244 United States |
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