JP Journal of Algebra, Number Theory and Applications
Volume 38, Issue 5, Pages 457 - 471
(October 2016) http://dx.doi.org/10.17654/NT038050457 |
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GALOIS GROUPS OF DEGREE 12 2-ADIC FIELDS WITH TRIVIAL AUTOMORPHISM GROUP
Chad Awtrey, Nicole E. Miles, Christoper Shill and Erin Strosnider
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Abstract: We focus on classifying degree 12 extensions of the 2-adic numbers that have a trivial automorphism group. For each extension, we compute a defining polynomial, the ramification index, residue degree, discriminant, and the Galois group of the normal closure. These results extend previous work in the area of constructive local field theory first initiated by Pauli-Roblot [14] and Jones-Roberts [8-10]. |
Keywords and phrases: 2-adic, extension fields, Galois group, local field. |
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