Let G be a p-solvable finite group for some prime p, \(G_{p'}\) a \(p'\)-Hall subgroup of G and x a p-regular element of G. Clearly, \(\langle x\rangle \le C_G(x)\le G\). Notice that the structure of \(G_{p'}\) is easily decided when \(C_G(x)=\langle x\rangle \) and \(C_G(x)=G\) for every p-regular element x of G. So, in this paper, we investigate the structure of \(G_{p'}\) by assuming that \(C_G(x)\) is maximal in G for every non-central p-regular element x of G.

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关于有限群中p-正则元素的扶正器

让ģ是p -solvable有限群对于一些素p，\（G_ {P '} \）一个\（P' \） -Hall的子组G ^和X一p的-regular元件ģ。显然，\（\ langle x \ rangle \ le C_G（x）\ le G \）。请注意，对于每个p-规则元素x，当\（C_G（x）= \ langle x \ rangle \）和\（C_G（x）= G \）时，很容易确定\（G_ {p'} \）的结构。的ģ。因此，在本文中，我们假设\（G_ {p'} \）的结构为\（C_G（X）\）为最大的G ^为每个非中央p -regular元件X的G ^。