00:01
Can we want to know how many elements of order two there are in various groups? we'll start with z16.
00:11
So z16 is the numbers from 0 to 15 under addition mod 16.
00:24
The only element of order two is 8, because 2 times anything else in here is not going to give us 16, which is 0, the identity.
00:37
Just for fun, the elements of order 4 are 4 and 12.
00:44
Of order 8 are 2, 6, 10, and 14, the other even numbers.
00:49
And the 16 is all the odd ones.
00:55
So that accounts for all of them.
01:00
The only element of order two is 8.
01:08
The next one we have z8 plus z2.
01:12
Okay, so we have two generators.
01:17
A has order 8, b has order 2...