IJPAM: Volume 100, No. 2 (2015)

DEGREE 14 EXTENSIONS OF $\mathbb{Q}_7$

Jim Brown$^1$, Robert Cass$^2$, Rodney Keaton$^3$,
Salvatore Parenti$^4$, Daniel Shankman$^5$
$^1$Department of Mathematical Sciences
Clemson University
Clemson, SC 29634, USA
$^2$Department of Mathematics
University of Kentucky
Lexington, KY 40506, USA
$^3$Department of Mathematics
University of Oklahoma
Norman, OK 73019, USA
$^4$Department of Mathematics
University of Michigan
Ann Arbor, MI 48109, USA
$^5$Department of Mathematics
University of Tennessee
Knoxville, TN 37996, USA

Abstract. We compute all degree 14 extensions of $\mathbb{Q}_7$ up to isomorphism, and find that there are 654 such extensions. Additionally, we compute several invariants of these extensions in order to classify the associated Galois group of the Galois closure of each extension.

Received: January 5, 2015

AMS Subject Classification: 11S15, 11S20

Key Words and Phrases: local fields, Galois groups

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DOI: 10.12732/ijpam.v100i2.12 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 100
Issue: 2
Pages: 337 - 345

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