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Order of an element in relation to the centre.

  1. Nov 2, 2008 #1
    If a is the only element of order 2 in a group, does it belong to the centre Z(G)?
     
  2. jcsd
  3. Nov 3, 2008 #2

    morphism

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  4. Nov 4, 2008 #3

    cup

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    Hint: In every group, there is always a certain special (and familiar) element, of order 2.
     
  5. Nov 4, 2008 #4

    morphism

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    Not true. If you're thinking of the identity element, then it has order 1.

    I don't want to give the OP any hints because he/she hasn't posted any work.
     
  6. Nov 4, 2008 #5

    cup

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    You are right, of course. How embarrassing...
     
  7. Nov 4, 2008 #6

    morphism

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    It happens to all of us! :wink:
     
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