00:01
So in this problem, we're asked to do the k -the -table for z2 cross z4.
00:20
With generators, a is 1 -0, and b is 0 ,1, under addition.
00:42
Okay, so let's first talk about what does this mean, z2 cross z4? well, z2 only has two elements, 0 and 1.
00:55
And z4 has 4 elements, 0, 1, 2, and 3.
01:00
So this means that i have an ordered pair now, where the first elements come from z2, and the second elements come from z4.
01:16
And then i'm going to do the kd table with those under addition.
01:21
Okay, so it's going to be.
01:28
Under addition then so what is this going to look like well it's going to look like zero zero see i start generating these ordered pairs here first of all zero one zero two and zero three and then i have one zero one one one two and one three and i have the same ordered pairs over here zero zero one zero one zero 2, 03, 1 -0, 1 -1, 1 -2, and 1 -3.
02:31
Okay, so now, addition.
02:34
So 0 added to anything is itself.
02:37
So this top row is going to just be these elements again, these ordered pairs again, because i'm not adding anything to them by adding 0 -0 to them, right? so i can just copy those down.
02:55
And the same thing happens in the first column.
02:57
This is 01, 02, 03, 1 -1, 1 -2, and 1 -3.
03:16
All right, now then, add 0 -1.
03:21
That means the second element gets a 1 added to it.
03:25
So this becomes 0 -2, this becomes 0 -3.
03:30
But now 3 plus 1 is 4.
03:33
Well 4 in z4 is 0 again.
03:36
So this is 0 .0.
03:39
And now i have 1 1, 1 2, 1 3, and 1 0 again, right? because 3 plus 1 would be 4, which is 0 in z4.
03:53
Okay.
03:55
Next row, i'm going to add 2 to the second element.
03:58
So this is 03, 0...