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Subgroups of Chevalley Groups Over Rings

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Let R be a commutative ring. The lattice of subgroups of a Chevalley group G(Φ,R) containing the subgroup D(R) is studied, where D is a subfunctor of G(Φ, — ). Assuming that over any field F the normalizer of the group D(F) is “closed to be maximal,” it is proved that under some technical conditions the lattice is standard. A condition, on the normalizer of D(R) is studied in the case, where D(R) is the elementary subgroup of another Chevalley group G(Ψ,R) embedded into G(Φ,R).

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Authors and Affiliations

  1. St.Petersburg State University; St.Petersburg Department of SteklovMathematical Institute, St.Petersburg, Russia

    R. Lubkov

  2. St.Petersburg State University, St.Petersburg, Russia

    A. Stepanov

Authors
  1. R. Lubkov
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  2. A. Stepanov
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Correspondence to R. Lubkov.

Additional information

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 484, 2019, pp. 121–137.

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Lubkov, R., Stepanov, A. Subgroups of Chevalley Groups Over Rings. J Math Sci 252, 829–840 (2021). https://doi.org/10.1007/s10958-021-05203-x

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  • DOI: https://doi.org/10.1007/s10958-021-05203-x

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