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

Rod Gow; Gary McGuire

paper

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

arXiv:2109.06693

Abstract

Let $F$ be any field. We give a short and elementary proof that any finite subgroup $G$ of $P G L (2, F)$ 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 $P G L (2, F)$ as Galois groups.

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

Abstract

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