Re: Centre of a group proof

You're supposed to *prove* that for all not assume and play around with it (a common mistake with many students). (Shake)

This is what you do. Let Show that order But is the unique element of order in What does this tell you? (Smile)

Re: Centre of a group proof

So you can say that since a is in the group then its conjugate must also be in the group, let b be its conjugate then

bb=g^{-1}agg^{-1}ag= g^{-1}aag=g^{-1}g= e so b also had order 2

Since a is the only element of order to b must be a

Does that look alright?

Re: Centre of a group proof

That's correct. One more line completes the proof. (Nod)

Re: Centre of a group proof

Thanks Sylvia!

Do you mean like, for the final line, a conclusion like,

Therefore as b = a, since the group has only one order 2 element,

b = g-1ag

gb=ag

ga=ag

and hence a is in the centre of G