Explicit realization of the Dickson groups G2(q) as Galois groups
TLDR
For any prime power q, the construction of a polynomial f q (X) ∈ F q (t,u)[X] whose Galois group over F q(t, u) is the Dickson group G 2 (q) has been studied in this paper.Abstract:
For any prime power q we determine a polynomial f q (X) ∈ F q (t,u)[X] whose Galois group over F q (t, u) is the Dickson group G 2 (q). The construction uses a criterion and a method due to Matzat.read more
Citations
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Book ChapterDOI
Frobenius modules and galois groups
TL;DR: Frobenius modules are finite-dimensional vector spaces over fields with a Frobenius endomorphism O, provided with an injective O-semilinear operator as discussed by the authors.
Journal ArticleDOI
Additive polynomials for finite groups of Lie type
Maximilian Albert,Annette Maier +1 more
TL;DR: In this article, a unified Galois group realization of all classical finite groups of Lie type as well as a number of exceptional ones (with low-dimensional representations) as Galois groups over function fields over F q is presented and explicit additive polynomials for the extensions.
Difference equations with semisimple Galois groups in positive characteristic
Annette Maier,Julia Hartmann +1 more
TL;DR: In this paper, it was shown that the special linear groups SLn, the symplectic groups Sp2d, the special orthogonal groups SOn (here we have to assume q odd), and the Dickson group G2 (in both cases q odd and even).
Journal ArticleDOI
Additive Polynomials for Finite Groups of Lie Type
Maximilian Albert,Annette Maier +1 more
TL;DR: In this article, the authors provide a unified approach based on results of Matzat which give bounds for Galois groups of Frobenius modules and use the structure and representation theory of corresponding connected linear algebraic groups.
Journal ArticleDOI
Rigid G 2-representations and motives of type G 2
TL;DR: In this article, the authors consider a family of motives associated to the rigid local system whose monodromy is dense in the simple algebraic group of type G2 and which has a local monodrome of order 7 at ∞, and prove an explicit Hilbert irreduciblity theorem for the associated etale realizations.
References
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The maximal subgroups of the chevalley groups G2(q) with q odd, the Ree groups 2G2(q), and their automorphism groups☆
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Unramified Coverings of the Affine Line in Positive Characteristic
TL;DR: In this article, it was shown that there is a finite unramified covering C of the affine line A1, defined over the field of p elements, so that A1 is the quotient of C by the fixed-point free action of SL n (Fpk).