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The finite subgroups of \({\text {SL}}(3,\overline{F})\)

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Abstract

We attempt to give a complete exposition of the classification of the finite subgroups of \({\text {SL}}(3,\overline{F})\), where \(\overline{F}\) is a separably closed field of characteristic not dividing the order of the finite group, in contemporary language, completing some of the proofs of Blichfeldt from the early twentieth century. The classification—originating from Jordan, Klein, Valentiner—has applications in algebraic geometry, number theory and mathematical physics.

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Acknowledgements

Partially supported by the Simons Foundation Grant #317731. I wish to express my deep gratitude to Ron Solomon for extensive and constructive correspondence in particular on Sect. 3, as well as to the Hebrew University in Jerusalem and IPMU at Tokyo University, where most of this work was done.

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  1. Ariel University, 40700, Ariel, Israel

    Yuval Z. Flicker

  2. The Ohio State University, Columbus, OH, 43210, USA

    Yuval Z. Flicker

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  1. Yuval Z. Flicker
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Correspondence to Yuval Z. Flicker.

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Communicated by Mikhail Belolipetsky.

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Flicker, Y.Z. The finite subgroups of \({\text {SL}}(3,\overline{F})\). São Paulo J. Math. Sci. 14, 407–436 (2020). https://doi.org/10.1007/s40863-020-00178-0

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