Let G be a finite abelian group and let x and y be elements

Let G be a finite abelian group and let x and y be elements of G. If the order of x is 4 and the order of y is 6, what is the order of xy?

10

24

12

6

Solution

Given O (x) = 4 , O(y) =6

the 2 elements x,y are in the group G and by closure property xy is also in G

and O (xy) = LCM ( 4,6) = 12

option 3) is correct