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Is there a way to prove that in a group of squarefree order Sylow subgroup corresponding to largest prime(which divides order of group) is normal without using transfer theory(and Burnside's theorem)?

Thanks in advance.

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    It would make more sense to learn Burnside's Transfer Theorem than to spend time trying to avoid it. – 2017-02-21
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    Yes, I agree, but I want to know if this can be proven without that theorem. – 2017-02-22

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