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Math Help - Sylow p-subgroups

  1. #1
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    Sylow p-subgroups

    Hello,

    I'm trying to show that if H is a subgroup of a finite group G, and p is a prime that the number of sylow p-subgroups of H n_H is less thanor equal to the number of sylow p-subgroups of n_G.

    This is all I have:
    Clearly if p does not divide |G| then p does not divide |H| and so n_H = n_G = 0. Let p^j and p^k be the greatest powers of p that divides |H| and |G| respectively.

    Case 1: j = k. In this case any sylow p-subgroup of H is a sylow p-subgroup of G and so clearly n_H \le n_G.

    Case 2: j < k.

    This is where i got stuck. I am at a point where I need to show that each sylow p-subgroup of G can contain only one sylow p-subgroup of H. I do not know if this is right path, maybe I overlooked a simple theorem.

    Any assistance is greatly appreciated. Thank you.

    m_s_d
    Last edited by math_science_dude; April 3rd 2008 at 09:32 PM. Reason: The part in italics reads entirely wrong. Sorry
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