IJPAM: Volume 70, No. 6 (2011)

ON GALOIS GROUPS OF TOTALLY AND TAMELY
RAMIFIED SEXTIC EXTENSIONS OF LOCAL FIELDS

Chad Awtrey
Department of Mathematics and Statistics
Elon University
Campus Box 2320, Elon, NC 27244, USA


Abstract. Let $K$ be a finite extension of the $p$-adic numbers with $p>3$ and $L/K$ a totally ramified sextic extension. For each of the sixteen transitive subgroups $G$ of $S_6$, we count the number of nonisomorphic extensions where the Galois group of the splitting field of $L$ is equal to $G$. 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