Order of an element in relation to the centre.

sairalouise · Nov 2, 2008

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

morphism · Nov 3, 2008

cup · Nov 4, 2008

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

morphism · Nov 4, 2008

cup said:

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 · Nov 4, 2008

morphism said:

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

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

morphism · Nov 4, 2008

cup said:

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

It happens to all of us!

Order of an element in relation to the centre.

Thread 'About the existence of Hamel basis for vector spaces'

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