If G is a group and , prove that ab and ba have the same order. I think i need to use the conjugate to prove this, because conjugate elements have the same order.
If G is a group and , prove that ab and ba have the same order. I think i need to use the conjugate to prove this, because conjugate elements have the same order.
--------------- Conjugate elements have the same order
As painfully and embarrasingly simple as that. Why, did you expect something very difficult?
And what did you mean in your last line ? This is not true, not even close, in general. What you sure meant is that either