IJPAM: Volume 75, No. 2 (2012)
Department of Mathematics and Statistics
Campus Box 2320, Elon, NC 27244, USA
Abstract. Let and be odd prime numbers. We study degree extensions of the -adic numbers whose normal closures have Galois group equal to , the dihedral group of order . If , the extensions are tamely ramified and are straightforward to classify; there is a unique such extension if and none otherwise. If , we follow Amano and show there are six such extensions if and three otherwise. For each extension, we provide a defining polynomial and compute its inertia subgroup.
Received: July 8, 2011
AMS Subject Classification: 11S05, 11S15, 11S20, 20B35
Key Words and Phrases: -adic, extension fields, Galois group, dihedral, inertia, ramification
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395