IJPAM: Volume 70, No. 6 (2011)
RAMIFIED SEXTIC EXTENSIONS OF LOCAL FIELDS
Department of Mathematics and Statistics
Campus Box 2320, Elon, NC 27244, USA
Abstract. Let be a finite extension of the -adic numbers with and a totally ramified sextic extension. For each of the sixteen transitive subgroups of , we count the number of nonisomorphic extensions where the Galois group of the splitting field of is equal to . The technique is new and is based on the mass formulas of Krasner and Serre.
Received: March 10, 2011
AMS Subject Classification: 11S15, 11S20
Key Words and Phrases: local fields, Galois groups
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395