IJPAM: Volume 104, No. 3 (2015)

ON GALOIS GROUPS OF DEGREE 15 POLYNOMIALS

Chad Awtrey$^1$ Mazur$^2$, Sara Rodgers$^3$, Nicole Soltz$^4$, Jesi Weed$^5$
$^{1,2,3,4,5}$Department of Mathematics and Statistics
Elon University
Campus Box 2320, Elon, NC 27244, USA


Abstract. We discuss the construction and factorization pattern of several resolvent polynomials that are useful for computing Galois groups of degree 15 polynomials. As an application, we develop an algorithm for computing the Galois group of a degree 15 polynomial defined over the 5-adic numbers. This algorithm is of interest since it uses substantially fewer resolvents than the traditional method for computing Galois groups.

Received: July 19, 2015

AMS Subject Classification: 11S15, 11S20

Key Words and Phrases: 5-adic, extension fields, Galois group, local field

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DOI: 10.12732/ijpam.v104i3.10 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 104
Issue: 3
Pages: 407 - 420


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