Order of an element in relation to the centre.

[sairalouise]

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

 

[morphism]

Yes.

 

[cup]

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

 

[morphism]

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.

 

[cup]

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

You are right, of course. How embarrassing...

 

[morphism]

You are right, of course. How embarrassing...

It happens to all of us!