I have this question which asks to prove that if a group has an element, a such that |a|=2, (exactly one order 2 element a) that this element is in the centre of the group.
so ag=ga for all g in G
aga-1=g, aa-1g=g so aa-1=e which is true since a has order 2.
But I feel like this isn't enough at all and I cant really see where the "exactly 1 element with |a|=2" comes in,
Does anyone have any ideas?