Elsevier

Advances in Mathematics

Volume 302, 22 October 2016, Pages 48-58
Advances in Mathematics

Rational rigidity for F4(p)

https://doi.org/10.1016/j.aim.2016.07.015Get rights and content
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Abstract

We prove the existence of certain rationally rigid triples in F4(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.

MSC

primary
12F12
20C33
secondary
20E28

Keywords

Inverse Galois problem
Rigidity
Lie primitive subgroups
Regular unipotent elements

Cited by (0)

Robert Guralnick was partially supported by the National Science Foundation grants FRG-1265297 and DMS-1302886. He also thanks the Simons Foundation for its support. This work was initiated in Spring 2013 when Robert Guralnick and Jun Yu were visiting the Institute for Advanced Study. They thank the Institute for its hospitality and support. We thank the referee for careful reading.