Section 7.1 (part 2) due 10/27

The section says that a nonzero ring is never a group because of the zero ring. Since multiplication is such a straightforward operation, why do they not make an exception in the group to say that for everything else, the group will work?

I thought the reflections were interesting because I haven't thought about reflections of shapes for a long time. I also think the theorems were somewhat interesting because they find some groups for us.