A Polynomial with Galois GroupSL2(11)

Abstract

We compute a polynomial with Galois group SL 2 (11) over Q. Furthermore we prove that SL 2 (11) is the Galois group of a regular extension of Q(t).

Multi-parameter Polynomials with Given Galois Group

“…Thus an L 2 (11) extension N/Q embeddable into an SL 2 (11) extension necessarily has to be totally real. It has recently been shown by Klüners (2000) that Serre's criterion (see, for example, Malle and Matzat, 1999, IV.6.3) applies to one of the totally real specializations of the polynomial f (a, t, X) in Theorem 9.1.…”

Covering groups of $M_{22}$ as regular Galois groups over $\mathbb{Q}$

“…Finally, the following is especially adapted to central embedding problems with kernel of order 2. It is contained (in a language of Brauer classes) in [16], and applied to obtain regular Galois realizations with group SL 2 (7) and 2.M 12 in [17] (see also [8] for an application to the group SL 2 (11)).…”

On Quadratic Number Fields Each Having an Unramified Extension Which Properly Contains the Hilbert Class Field of its Genus Field

“…is a real quadratic-ramified PSL(2, ll)-extension of Q, in which only the 'This polynomial is found also in [12). in any field of degree 11 defined by this polynomial is 1 2 1 2 12 2 2.)…”