Abstract
Let p be a prime number and n a positive integer. In recent years, several authors have focused on classifying degree n extensions of the p-adic numbers; the most difficult cases arising when p∣n and n is composite. Since current research has dealt with n ≤ 10 when p = 2n, this paper considers degree 12 extensions of the 2-adic numbers. Focusing on extensions whose automorphism groups have order 6 or 12, we compute the Galois group of each extension (or of the normal closure for non-Galois extensions) and identify the group as a transitive subgroup of S 12. Our method for computing Galois groups is of interest, since it does not involve factoring resolvent polynomials (which is the traditional approach).
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Acknowledgments
The authors would like to thank the anonymous reviewer for his/her helpful comments. The authors would also like to thank Elon University for supporting this project through internal grants.
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Awtrey, C., Shill, C.R. (2013). Galois Groups of 2-Adic Fields of Degree 12 with Automorphism Group of Order 6 and 12. In: Rychtář, J., Gupta, S., Shivaji, R., Chhetri, M. (eds) Topics from the 8th Annual UNCG Regional Mathematics and Statistics Conference. Springer Proceedings in Mathematics & Statistics, vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9332-7_7
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DOI: https://doi.org/10.1007/978-1-4614-9332-7_7
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