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On Some Automorphisms of Orthogonal Groups in Odd Characteristic

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In this paper, it is proved that the simple orthogonal groups O 2n+1(q) and O ±2n (q) (where q is odd) cannot be automorphism groups of finite left distributive quasigroups. This is a particular case of the conjecture stating that the automorphism group of a left distributive quasigroup is solvable. To complete the proof of the conjecture, one must test all finite groups.

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Authors and Affiliations

  1. Russia

    V. M. Galkin & N. V. Mokhnina

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  1. V. M. Galkin
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  2. N. V. Mokhnina
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Galkin, V.M., Mokhnina, N.V. On Some Automorphisms of Orthogonal Groups in Odd Characteristic. Mathematical Notes 70, 25–34 (2001). https://doi.org/10.1023/A:1010261515666

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  • DOI: https://doi.org/10.1023/A:1010261515666

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