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Let $U$ and $S$ be two maximal subgroups of a finite group $G$ such that $Core_G(U)\ne Core_G(S)$ and both $U$ and $S$ supplement a chief factor $H/K$.

Let $M=(U\cap S)H$. Prove that $M$ is maximal in $G$ and $Core_G(M)=(Core_G(U)\cap Core_G(S))H$.

Thanks in advance.

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 Reads like homework. Please read the FAQ. – José Figueroa-O'Farrill Nov 11 2010 at 23:44
No, this question is not a homework. I read some books, it is one theorem. But I does not like the way of proving in that book. I want to prove it directly but it seemed that I could not fine a right way. – john peter Nov 12 2010 at 13:29

closed as too localized by José Figueroa-O'Farrill, Yemon Choi, Simon Thomas, Andy Putman, Andreas Thom Nov 12 2010 at 9:27

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