Abstract:In the present paper, a description of overgroups for the subsystem subgroups $E(\Delta ,R)$ of the Chevalley groups $G(\Phi ,R)$ over the ring $R$, where $\Phi$ is a simply laced root system and $\Delta$ is its sufficiently large subsystem, is almost entirely finished. Namely, objects called levels are defined and it is shown that for any such overgroup $H$ there exists a unique level $\sigma$ with $E(\sigma )\le H\le \operatorname {Stab}_{G(\Phi ,R)}(L_{\max }(\sigma ))$, where $E(\sigma )$ is an elementary subgroup associated with the level $\sigma$ and $L_{\max }(\sigma )$ is the corresponding subalgebra of the Chevalley algebra. Unlike the previous papers, here levels can be more complicated than nets of ideals.

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中文翻译：

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异常群中子系统子群的超群：非理想水平

摘要：本文描述了 Chevalley 群 $G(\Phi ,R)$ 在环 $R$ 上的子系统子群 $E(\Delta ,R)$ 的超群，其中 $\Phi$ 是一个简单的根系统和 $\Delta$ 是它足够大的子系统，几乎完全完成了。即，定义了称为水平的对象，并且表明对于任何这样的超群 $H$ 存在一个唯一的水平 $\sigma$ 和 $E(\sigma )\le H\le \operatorname {Stab}_{G(\ Phi ,R)}(L_{\max }(\sigma ))$，其中 $E(\sigma )$ 是与级别 $\sigma$ 和 $L_{\max }(\sigma )$ 关联的初等子群是 Chevalley 代数的相应子代数。与之前的论文不同，这里的层次可能比理想网更复杂。

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