JP Journal of Algebra, Number Theory and Applications
Volume 44, Issue 2, Pages 201 - 210
(November 2019) http://dx.doi.org/10.17654/NT044020201 |
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AUTOMORPHISMS OF 2-ADIC FIELDS OF DEGREE TWICE AN ODD NUMBER
Chad Awtrey and Briana Brady
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Abstract: Let n > 0 be an odd integer. We show that every totally ramified extension of the 2-adic numbers of degree 2n has two automorphisms. When combined with Krasner’s Mass Formula, this allows us to count isomorphism classes of totally ramified 2-adic fields of degree 2n by discriminant. We further provide canonical defining Eisenstein polynomials for each extension. These results generalize previous work, which focused on the specific cases where n ≤ 7. |
Keywords and phrases: Eisenstein polynomials, p-adic fields, automorphism groups, totally ramified extensions.
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