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I want to prove Lemma 2.1(1) in the paper On X-s-Permutable Subgroups of a Finite Group by Min Bang SU, Yang Ming LI. It is on the web. This is my proof. . Since $H$ is $X−s−$permutable in $G$, then for $P$ Sylow of $G$ there exists $x \in X$ such that $P^{x}H=HP^{x}$. The Sylow of $N$ are of the form $P∩N$. Thus,$(P∩N)^{x}H=H(P∩N)^{x}$. Hence, $H$ is $X−s−$permutable in $N$.

The problem is, according to the definition in the second page, that $X \subseteq G$ but in my proof $X$ may not be a subset of $N$.

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It would be better if you gave a reference for the paper. – HJRW Apr 23 '12 at 14:11
I believe it is "On X-s-permutable subgroups of a finite group", by Min Ban Su and Yang Ming Li. But the question is still inappropriate. Voting to close. – Igor Rivin Apr 23 '12 at 14:18
Sorry, if I have done something wrong. – moont14263 Apr 23 '12 at 14:27
The question falls under the rubric of "too localized" -- proving lemmas in papers is not of general interest... – Igor Rivin Apr 23 '12 at 14:32
I think the post falls into the category of "not a well posed question". If it could be made clear and specific as to what is desired, as well as what has been tried, such a revised question might be suitable for MathOverflow. Gerhard "Ask Me About System Design" Paseman, 2012.04.23 – Gerhard Paseman Apr 23 '12 at 16:28

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