Products and commutators of classes in algebraic groups

2013/02/01 by Robert M. Guralnick, Guralnick, Robert, Gunter Malle +1
Mathematics · #20E45 #20F12 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Primary 20G07 #Secondary 20E32

paper · pdf · doi:10.48550/arxiv.1302.0182

openalex publication_date 2013/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify pairs of conjugacy classes in almost simple algebraic groups whose product consists of finitely many classes. This leads to several interesting families of examples which are related to a generalization of the Baer--Suzuki theorem for finite groups. We also answer a question of Pavel Shumyatsky on commutators of pairs of conjugacy classes in simple algebraic groups. It turns out that the resulting examples are exactly those for which the product also consists of only finitely many classes.

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