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Homework Help: Show these are subgroups of a group G?

  1. Feb 15, 2010 #1
    Z(G) = { x in G : xg=gx for all g in G } (center of a group G)

    and

    C(g) = { x in G : xg=gx } (centralizer of g in G)


    Z(G) is a subgroup by the proof here:

    http://en.wikipedia.org/wiki/Center_(group_theory)#As_a_subgroup


    How do I go about showing C(g) is a subgroup? The proofs look like they should be identical to me, but then why do I have 2 seperate questions for it?

    Thanks
     
    Last edited: Feb 15, 2010
  2. jcsd
  3. Feb 15, 2010 #2

    Dick

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    They are two different questions because Z(G) is not the same thing as C(g). Yes, the proofs are almost identical. So just go ahead and prove C(g) is a group.
     
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