Thread: usng a conjugate

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.

Originally Posted by ux0

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.

Tonio

its just that simple?



---------Multiplication of the identity

---------- Associativity

--------------- Conjugate elements have the same order

Originally Posted by ux0

its just that simple?



---------Multiplication of the identity

---------- Associativity

--------------- 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

Tonio

Ya I kind of did, and thanks for the notation correction!