Question

If a is a group element and a has infinite order, prove that am ? an

when m ? n.​

Answer 1

f a is a group element and a has infinite order, prove that m = n =⇒ am = an. (3 points) The fact that a has infinite order implies that a = e. If we had am = an then am-n = e. This would imply that a has finite order (some integer less than or equal to m − n).