00:01
All right, so for this problem, we're letting g be infinite cyclic.
00:10
So let's let a in g be a generator.
00:21
So this means that g is literally just as a set all the powers a to the n, such that n is in z.
00:30
So if i put a negative power, i interpret that as the inverse being multiplied that many times.
00:37
Okay.
00:39
So, let's define a map, fee, from g to z.
00:48
And what we're going to do is we're going to send a to the n to, well, n.
00:56
Okay? then, let's check that this is a homomorphism.
01:09
So this product will be the same thing as fee of a to the n plus m.
01:15
These exponent rules still work in groups.
01:19
So that's n plus m.
01:23
And that is fee of a to the n times.
01:30
So here i'm switching between two different notations.
01:34
In z, i use plus for my group operation...