It's a good thing I'm doing this review. I'm running into all kinds of stuff that I had skipped over.

I am constructing a quotient group of :

Let

I constructed the multiplication table as usual. Now I take the subgroup and construct . I get the cosets

Now I want to construct the multiplication table for , but when I apply the definition I get an apparent problem:

but

I would have expected both answers to be B, the inverse of A under the group . What did I do wrong?

Thanks!

-Dan