Abstract Let be the finite simply connected version of an exceptional Chevalley group, and let V be a nontrivial irreducible module, of minimal dimension, for over its field of definition. We explore the overgroup structure of in and the submodule structure of the exterior square (and sometimes the third Lie power) of V. When is defined over a field of odd prime order p, this allows us to construct the smallest (with respect to certain properties) p-groups P such that the group induced by on is either or its normalizer in

中文翻译：

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关于具有与异常 Chevalley 群相关的自同构群的 p 群

摘要 令 为异常 Chevalley 群的有限单连通版本，令 V 为非平凡不可约模，具有最小维数，在其定义域上。我们探索了 in 的超群结构和 V 的外部平方（有时是三次 Lie 幂）的子模结构。当在奇素数阶 p 的域上定义时，这允许我们构造最小的（关于某些属性) p-groups P 使得由 on 诱导的组是或者它的归一化器在