Subring subgroups of symplectic groups in characteristic 2

Bak A, Stepanov A (2017)
St. Petersburg Mathematical Journal 28(4): 465-475.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Bak, AnthonyUniBi; Stepanov, A.
Abstract / Bemerkung
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 subset of A provided Phi = B-n, C-n, or F-4, n >= 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 subset of R subset of A. In the present paper, a similar result is proved in the case where Phi = C-n, n >= 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 subset of Lambda subset of R subset of A. The result generalizes Ya. N. Nuzhin's theorem of 2013 concerning the root systems Phi = B-n, Cn, n >= 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.
Stichworte
Symplectic group; commutative ring; subgroup lattice; Bak unitary group; group identity with constants; small unipotent element; nilpotent; structure of K1
Erscheinungsjahr
2017
Zeitschriftentitel
St. Petersburg Mathematical Journal
Band
28
Ausgabe
4
Seite(n)
465-475
ISSN
1061-0022
eISSN
1547-7371
Page URI
https://pub.uni-bielefeld.de/record/2916594

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Bak A, Stepanov A. Subring subgroups of symplectic groups in characteristic 2. St. Petersburg Mathematical Journal. 2017;28(4):465-475.
Bak, A., & Stepanov, A. (2017). Subring subgroups of symplectic groups in characteristic 2. St. Petersburg Mathematical Journal, 28(4), 465-475. doi:10.1090/spmj/1459
Bak, A., and Stepanov, A. (2017). Subring subgroups of symplectic groups in characteristic 2. St. Petersburg Mathematical Journal 28, 465-475.
Bak, A., & Stepanov, A., 2017. Subring subgroups of symplectic groups in characteristic 2. St. Petersburg Mathematical Journal, 28(4), p 465-475.
A. Bak and A. Stepanov, “Subring subgroups of symplectic groups in characteristic 2”, St. Petersburg Mathematical Journal, vol. 28, 2017, pp. 465-475.
Bak, A., Stepanov, A.: Subring subgroups of symplectic groups in characteristic 2. St. Petersburg Mathematical Journal. 28, 465-475 (2017).
Bak, Anthony, and Stepanov, A. “Subring subgroups of symplectic groups in characteristic 2”. St. Petersburg Mathematical Journal 28.4 (2017): 465-475.

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