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ЖУРНАЛЫ // Алгебра и анализ // Архив

Алгебра и анализ, 2016, том 28, выпуск 4, страницы 47–61 (Mi aa1501)

Эта публикация цитируется в 3 статьях

Статьи

Subring subgroups of symplectic groups in characteristic 2

A. Baka, A. Stepanovbc

a Bielefeld University, Postfach 100131, 33501, Bielefeld, Germany
b St. Petersburg Electrotechnical University, Russia
c St. Petersburg State University, Faculty of Mathematics and Mechanics, 198504, St. Petersburg, Petrodvorets, Universitetskiĭ pr., 28, Russia

Аннотация: 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 $F_4$, $n\ge2$, 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 $\Phi=C_n$, $n\ge3$, 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 $\Phi=B_n$, $C_n$, $n\ge3$, 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 $K$.

Ключевые слова: symplectic group, commutative ring, subgroup lattice, Bak unitary group, group identity with constants, small unipotent element, nilpotent structure of $K1$.

Поступила в редакцию: 01.02.2016

Язык публикации: английский


 Англоязычная версия: St. Petersburg Mathematical Journal, 2017, 28:4, 465–475

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