My problem is slightly convoluted: The resource from which I am mainly following, has not introduced Orbit Stabilizer Theorem and have gone for proving it(Sylow) in a highly complex way. In short: I have lost patience with it.

However I have gone through the results and would like to apply it, to solve a few simple problems on my own.

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The chapters/topics before the topic covering Sylow THeorem doesnt cover Orbit Stabilizer Theorem. Without this tool, they have gone for proving Sylow theorem in a highly convoluted way – Soham Sep 27 '12 at 0:46
It seems you are aware of other proofs. Why not just read up on orbit-stabilizer and then grab a different text for the proof of Sylow? Basically any algebra text (apparently aside from yours) should do the trick. – Mike B Sep 27 '12 at 0:54

This is of course a matter of opinion, but I see no reason at all you shouldn't learn to apply Sylow's theorem before you learn to prove it. In more elementary areas of math we always do this, and the proving is almost an independent skill from the computing of Sylow $p$-subgroups.