Rational rigidity for F₄(p)

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• 作者：Robert M. Guralnick^a ; ^{guralnic@usc.edu" class="auth_mail" title="E-mail the corresponding author} ; Frank Lü ; beck^b ; ^{Frank.Luebeck@math.rwth-aachen.de" class="auth_mail" title="E-mail the corresponding author} ; Jun Yu^c ; ^{junyu@math.pku.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 12F12 ; 20C33 ; secondary ; 20E28
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：22 October 2016
• 年：2016
• 卷：302
• 期：Complete
• 页码：48-58
• 全文大小：337 K

文摘

We prove the existence of certain rationally rigid triples in F₄(p)$F_4(p)$ for good primes p   (i.e., 52c402" title="Click to view the MathML source">p>3$p>3$), thereby showing that these groups occur as regular Galois groups over Q(t)$\mathbb{Q}(t)$ and so also over Q$\mathbb{Q}$. 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.