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I Notation N(H) for a subgroup

  1. Oct 28, 2016 #1
    Hello! I have this problem:

    If H is a subgroup of prime index in a finite group G, show that either H is a normal subgroup or N(H) = H.

    What does N(H) means? I don't want a solution for the problem (at least not yet), I just want to know what that notation means. Thank you!
     
  2. jcsd
  3. Oct 28, 2016 #2

    fresh_42

    Staff: Mentor

    N(H) or better ##N_G(H)## is very likely the normalizer of ##H## in ##G##.
    That is ##N_G(H)=\{g \in G \,\vert \, gHg^{-1} \subseteq H\}\,##.
    The task here is to show that either ##N_G(H)=G## or ##N_G(H)=H\,##.
    The first means a normal subgroup, the latter is called a self-normalizing subgroup.
     
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