Question

give an example of a group in which there exists elements a,b such that o(a), o(b) are finite but o(ab) is not finite

Answer 1

o(a,b)=22,1/7

we take o(a)=22

and o(b)=1/7

we get o(a,b)=(22/7)

as we know that 22/7=3.142857143..............

hence we get an infinite number by group of finite numbers

Answer 2

Answer:

I hope this example is helpful for you.