Subring subgroups of symplectic groups in characteristic 2
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- by A. Bak and A. Stepanov
- St. Petersburg Math. J. 28 (2017), 465-475
- DOI: https://doi.org/10.1090/spmj/1459
- Published electronically: May 4, 2017
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Abstract:
In 2012, the second author obtained a description of the lattice of subgroups of a Chevalley group $G(\Phi ,A)$ that contain the elementary subgroup $E(\Phi ,K)$ over a subring $K\subseteq A$ provided $\Phi =B_n,$ $C_n$, or $F_4$, $n\ge 2$, and $2$ is invertible in $K$. It turned out that this lattice is a disjoint union of “sandwiches” parametrized by the subrings $R$ such that $K\subseteq R\subseteq A$. In the present paper, a similar result is proved in the case where $\Phi =C_n$, $n\ge 3$, and $2=0$ in $K$. In this setting, more sandwiches are needed, namely those parametrized by the form rings $(R,\Lambda )$ such that $K\subseteq \Lambda \subseteq R\subseteq A$. The result generalizes Ya. N. Nuzhin’s theorem of 2013 concerning the root systems $\Phi =B_n,$ $C_n$, $n\ge 3$, where the same description of the subgroup lattice is obtained, but under the condition that $A$ and $K$ are fields such that $A$ is algebraic over $K$.References
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Bibliographic Information
- A. Bak
- Affiliation: Bielefeld University, Postfach 100131, 33501 Bielefeld, Germany
- Email: bak@mathematik.uni-bielefeld.de
- A. Stepanov
- Affiliation: Mathematics and Mechanics Department, St. Petersburg State University, Universitetskiĭ pr. 28, 198504 St. Petersburg; St. Petersburg Electrotechnical University, Russia
- Email: stepanov239@gmail.com
- Received by editor(s): February 1, 2016
- Published electronically: May 4, 2017
- Additional Notes: The second author was supported by Russian Science Foundation, grant no. 14-11-00297
- © Copyright 2017 American Mathematical Society
- Journal: St. Petersburg Math. J. 28 (2017), 465-475
- MSC (2010): Primary 14L15
- DOI: https://doi.org/10.1090/spmj/1459
- MathSciNet review: 3604296