Author:
Guralnick Robert,Malle Gunter
Abstract
AbstractWe prove the existence of certain rationally rigid triples in${E}_{8}(p)$for good primes$p$(i.e. $p>5$) thereby showing that these groups occur as Galois groups over the field of rational numbers. We show that these triples arise from rigid triples in the algebraic group and prove that they generate an interesting subgroup in characteristic zero. As a byproduct of the proof, we derive a remarkable symmetry between the character table of a finite reductive group and that of its dual group. We also give a short list of possible overgroups of regular unipotent elements in simple exceptional groups.
Subject
Algebra and Number Theory
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