Order of an element in relation to the centre.

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

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  • #2
morphism
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Yes.
 
  • #3
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Hint: In every group, there is always a certain special (and familiar) element, of order 2.
 
  • #4
morphism
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Hint: In every group, there is always a certain special (and familiar) element, of order 2.
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.
 
  • #5
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Not true. If you're thinking of the identity element, then it has order 1.
You are right, of course. How embarrassing...
 
  • #6
morphism
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You are right, of course. How embarrassing...
It happens to all of us! :wink:
 

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