00:01
Um, yeah, so the group, um, z2 cross z4, um, consists of the ordered pairs where the first element comes from z2, which is just the set 0, 1, and the second element comes from z4, which is the set 0, 1, 2, 3.
00:16
So to list the elements of z2 cross z4, we just combine each of the elements of z2 with each of the elements in z4.
00:24
So the elements are going to be 0, 0 and then 0, 1 and then 0, 2 and 0, 3.
00:33
And then with the first element being 1, we have 1, 0, 1, 1, 1, 2 and 1, 3.
00:43
Now to find the order of each element, we just determine the smallest positive integer n such that n times a mod 2 and n b mod 4 equals 0, 0...