R\'ealisations galoisiennes explicites de certaines familles de $2$-groupes
Angelot Behajaina

TL;DR
This paper constructs explicit Galois extensions over rational function fields for certain 2-groups and identifies specializations that yield Galois groups over the rationals, advancing explicit realization techniques.
Contribution
It provides explicit constructions of Galois extensions with specified 2-group Galois groups and identifies arithmetic progressions for specializations over .
Findings
Explicit Galois extensions for certain 2-groups over (T)
Arithmetic progressions of integers with prescribed Galois groups
Method for realizing specific 2-groups as Galois groups over
Abstract
In this paper, we construct, for some -groups , explicit Galois extensions of group with . We also provide explicit arithmetic progressions of integers such that the specialization of at has Galois group .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Finite Group Theory Research
