Vol. 8, No. 2, 2015

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ISSN: 1944-4184 (e-only)
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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
Abstract

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 S14 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
Mathematical Subject Classification 2010
Primary: 11S15, 11S20
Milestones
Received: 11 August 2013
Revised: 28 August 2013
Accepted: 29 August 2013
Published: 3 March 2015

Communicated by Nigel Boston
Authors
Chad Awtrey
Department of Mathematics and Statistics
Elon University
Campus Box 2320
Elon, NC 27244
United States
Nicole Miles
Department of Mathematics and Statistics
Elon University
Campus Box 3753
Elon, NC 27244
United States
Jonathan Milstead
Department of Mathematics and Statistics
University of North Carolina
116 Petty Building
317 College Ave
Greensboro, NC 27412
United States
Christopher Shill
Department of Mathematics and Statistics
Elon University
Campus Box 9017
Elon, NC 27244
United States
Erin Strosnider
Department of Mathematics and Statistics
Elon University
Campus Box 5470
Elon, NC 27244
United States