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arXiv:2109.06693 [math.NT]AbstractReferencesReviewsResources

On the realization of subgroups of $PGL(2,F)$, and their automorphism groups, as Galois groups over function fields

Rod Gow, Gary McGuire

Published 2021-09-14Version 1

Let $F$ be any field. We give a short and elementary proof that any finite subgroup $G$ of $PGL(2,F)$ occurs as a Galois group over the function field $F(x)$. We also develop a theory of descent to subfields of $F$. This enables us to realize the automorphism groups of finite subgroups of $PGL(2,F)$ as Galois groups.

Categories: math.NT, math.AG, math.GR
Subjects: 12F12, 11S20
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