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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Acknowledgments
The first author was partially supported by the NSF grants DMS-1001962, DMS-1302886 and the Simons Foundation Fellowship 224965. The second author gratefully acknowledges financial support by ERC Advanced Grant 291512.
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Dedicated to the memory of Tonny Springer.
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Guralnick, R., Malle, G. Products and commutators of classes in algebraic groups. Math. Ann. 362, 743–771 (2015). https://doi.org/10.1007/s00208-014-1128-1
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DOI: https://doi.org/10.1007/s00208-014-1128-1