#### 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 $P\in ℂ\left[X\right]$ of degree $\mathfrak{2}\mathfrak{3}$ such that the Galois group of $P\left(x\right)-t$ over $ℂ\left(t\right)$ is the Mathieu group ${M}_{\mathfrak{2}\mathfrak{3}}$. This completes the computation of polyomials $P$ for which the Galois group of $P\left(x\right)-t$ is among the exceptional groups listed by Müller.

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