Rigidity for F_4(p)

TL;DR

This paper demonstrates the existence of rationally rigid triples in F_4(p) for good primes, establishing their role as Galois groups over Q(t) and revealing their algebraic and subgroup properties.

Contribution

It introduces new rationally rigid triples in F_4(p) for primes p > 3, linking them to Galois groups over Q and analyzing their algebraic structure.

Findings

Existence of rationally rigid triples in F_4(p) for p > 3

Realization of these triples as Galois groups over Q(t)

Identification of interesting subgroups generated by these triples

Abstract

We prove the existence of certain rationally rigid triples in F_4(p) for good primes p (i.e., p>3), thereby showing that these groups occur as regular Galois groups over Q(t) and so also over Q. We show that these triples give rise to rigid triples in the algebraic group and prove that they generate an interesting subgroup in characteristic 0.