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

- Thread starter sairalouise
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- #1

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

- #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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Not true. If you're thinking of the identity element, then it has order 1.Hint: In every group, there is always a certain special (and familiar) element, of order 2.

I don't want to give the OP any hints because he/she hasn't posted any work.

- #5

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You are right, of course. How embarrassing...Not true. If you're thinking of the identity element, then it has order 1.

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