Vol. 1, No. 1, 2013

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The complex polynomials $P(x)$ with $\mathop{\rm Gal}(P(x)-t) \cong M_{23}$

Noam D. Elkies

Vol. 1 (2013), No. 1, 359–367
Abstract

We find the polynomials P [X] of degree 23 such that the Galois group of P(x) t over (t) is the Mathieu group M23. This completes the computation of polyomials P for which the Galois group of P(x) t is among the exceptional groups listed by Müller.

Keywords
Mathieu group $M_{23}$, Galois groups, Chebotarev density theorem
Mathematical Subject Classification 2010
Primary: 12F12
Secondary: 20D08
Milestones
Published: 14 November 2013
Authors
Noam D. Elkies
Department of Mathematics
Harvard University
Cambridge, MA 02138
United States