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Galois groups of polynomials arising from circulant matrices |
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| Authors: | M. Filaseta F. Luca |
| Affiliation: | a Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA b IMATE, UNAM, Ap. Postal 61-3 (Xangari), CP. 58 089, Morelia, Michoacán, Mexico c Department of Applied Mathematics, GSEAS, Naval Postgraduate School, 833 Dyer Road, Monterey, CA 93943, USA d Department of Mathematics, Auburn University Montgomery, Montgomery, AL 36124, USA |
| Abstract: | Circulant matrices are used to construct polynomials, associated with Chebyshev polynomials of the first kind, whose roots are real and made explicit. Then the Galois groups of the polynomials are computed, giving rise to new examples of polynomials with cyclic Galois groups and Galois groups of order p(p−1) that are generated by a cycle of length p and a cycle of length p−1. |
| Keywords: | Galois group Chebyshev polynomial Dickson polynomial Irreducible polynomial |
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