IJPAM: Volume 70, No. 6 (2011)
ON GALOIS GROUPS OF TOTALLY AND TAMELY
RAMIFIED SEXTIC EXTENSIONS OF LOCAL FIELDS
RAMIFIED SEXTIC EXTENSIONS OF LOCAL FIELDS
Chad Awtrey
Department of Mathematics and Statistics
Elon University
Campus Box 2320, Elon, NC 27244, USA
Department of Mathematics and Statistics
Elon University
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
Year: 2011
Volume: 70
Issue: 6