Abstract We continue the project started in [8] to describe the structure of the finite groups G of characteristic p in terms of their Baumann components and the conjugacy class Bau p ( G ) . The reduction theorem proved in [8] allows to assume that G has a unique Baumann component. In this paper we use this property to determine the isomorphism type of G / O p ( G ) and the action of G on Ω 1 ( Z ( O p ( G ) ) ) . In addition, we prove reduction theorems which allow to focus on groups G which satisfy G / O p ( G ) ≅ SL n ( q ) , Sp 2 n ( q ) or G 2 ( q ) and O p ( G ) ⩽ B for B ∈ Bau p ( G ) .

中文翻译：

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特征 p 的有限群的鲍曼分量，约简定理

摘要 我们继续在 [8] 中开始的项目，用它们的鲍曼分量和共轭类 Bau p ( G ) 来描述特征 p 的有限群 G 的结构。[8] 中证明的约简定理允许假设 G 具有唯一的 Baumann 分量。本文利用这个性质来确定G/O p(G)的同构类型和G对Ω1(Z(Op(G)))的作用。此外，我们证明了简化定理，它允许关注满足 G / O p ( G ) ≅ SL n ( q ) ，Sp 2 n ( q ) 或 G 2 ( q ) 和 O p ( G ) ⩽ B 的群 G对于 B ∈ Bau p ( G ) 。