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A Linear Resolvent for Degree 14 Polynomials

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Collaborative Mathematics and Statistics Research

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 109))

Abstract

We discuss the construction and factorization pattern of a linear resolvent polynomial that is useful for computing Galois groups of degree 14 polynomials. As an application, we develop an algorithm for computing the Galois group of a degree 14 polynomial defined over the 7-adic numbers. This algorithm is of interest since it only makes use of the aforementioned linear resolvent, the polynomial’s discriminant, and subfield information of the polynomial’s stem field.

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Acknowledgements

The authors would like to thank Elon University for supporting this project through internal grants and the Center for Undergraduate Research in Mathematics for their grant support. This research was supported in part by NSF grant # DMS-1148695.

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Authors and Affiliations

  1. Elon University, Campus Box 2320, Elon, NC, 27244, USA

    Chad Awtrey & Erin Strosnider

Authors
  1. Chad Awtrey
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  2. Erin Strosnider
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Corresponding author

Correspondence to Chad Awtrey .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics & Statistics, University of North Carolina Greensboro, Greensboro, North Carolina, USA

    Jan Rychtář

  2. Dept. of Mathematics & Statistics, University of North Carolina Greensboro, Greensboro, North Carolina, USA

    Maya Chhetri

  3. Dept. of Mathematics & Statistics, University of North Carolina Greensboro, Greensboro, North Carolina, USA

    Sat Gupta

  4. Dept. of Mathematics & Statistics, University of North Carolina Greensboro, Greensboro, North Carolina, USA

    Ratnasingham Shivaji

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Awtrey, C., Strosnider, E. (2015). A Linear Resolvent for Degree 14 Polynomials. In: Rychtář, J., Chhetri, M., Gupta, S., Shivaji, R. (eds) Collaborative Mathematics and Statistics Research. Springer Proceedings in Mathematics & Statistics, vol 109. Springer, Cham. https://doi.org/10.1007/978-3-319-11125-4_5

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