# Subring subgroups in symplectic groups in characteristic 2

@article{Bak2015SubringSI, title={Subring subgroups in symplectic groups in characteristic 2}, author={Anthony Bak and A. Stepanov}, journal={arXiv: Rings and Algebras}, year={2015} }

In 2012 the second author obtained a description of the lattice of subgroupsof a Chevalley group $G(\Phi,A)$, containing 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 turns out that this lattice splits into a disjoint union of "sandwiches", parametrized by intermediate subrings between $K$ and $A$.
In the current article a similar result is proved for $\Phi=B_n$ or $C_n$, $n\ge3$, and $2=0$ in $K…

## 4 Citations

### Subgroups of Chevalley groups of types $B_l$ and $C_l$ containing the group over a subring, and corresponding carpets

- MathematicsSt. Petersburg Mathematical Journal
- 2020

We continue study of subgroups of a Chevalley group $G_P(\Phi,R)$ over a ring $R$ with a root system $\Phi$ and a weight lattice $P$, containing the elementary subgroup $E_P(\Phi,K)$ over a subring…

### The Normalizer of the Elementary Linear Group of a Module Arising when the Base Ring is Extended

- MathematicsJournal of Mathematical Sciences
- 2018

Let S be a commutative ring with 1 and R a unital subring. Let M be a free S-module of rank n ≥ 3. In 1994, V. A. Koibaev described the normalizer of AutS(M) in the group AutR(M). In the present…

### Suzuki–Ree groups and Tits mixed groups over rings

- MathematicsCommunications in Algebra
- 2019

Abstract It is shown that Suzuki–Ree groups can be easily defined by means of comparing two fundamental representations of the ambient Chevalley group in characteristic 2 or 3. This eliminates the…

### The Normalizer of the Elementary Linear Group of a Module Arising when the Base Ring is Extended

- MathematicsJournal of Mathematical Sciences
- 2018

Let S be a commutative ring with 1 and R a unital subring. Let M be a free S-module of rank n ≥ 3. In 1994, V. A. Koibaev described the normalizer of AutS(M) in the group AutR(M). In the present…

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