Thread: Factor group of an external direct product

Find the order of

Now, the elements in are (0,0) and (1,1), so the order of it is 2. but I'm confuse about the second one, what is the order of that?

Originally Posted by tttcomrader

Find the order of

Now, the elements in are (0,0) and (1,1), so the order of it is 2. but I'm confuse about the second one, what is the order of that?

Here
Write out which means .
Now notice that,
.
Form a complete list of co-sets, i.e. the even ones and the odd ones.
Thus, this factor group is of order 2.