00:01
Okay, so let's get started with part a of this exercise.
00:05
Well, here we are gonna have a subgroup for each divisor of 20.
00:12
Now we can write 20 as 2 squared multiplied by 5.
00:19
So we have the following devices.
00:22
So devices.
00:25
Okay, so the devices are 2, 4, 10 and oh maybe let me write 5 first okay 5 10 and 20 itself perfect so here we are going to have the following subgroups so subgroups okay so our subgroups are going to be the subgroup generated by 2 the subgroup generated by 4 the subgroup generated by 5, the subgroup generated by 10, and then we are going to have the trivial subgroups, that is our group z20 itself, and the subgroup generated by 0, which is 0 only.
01:23
Perfect.
01:24
Now, we need, this one was part a of our exercise.
01:32
For part b of our exercise, well, here we need h with the order of h equals five and well what is such a subgroup clearly we are gonna have the subgroup generated by four okay perfect now okay this is part c clearly the cosets of h form a group so let me write like this cosets of of h...