Difficult: I didn't have much difficulty with this section; in fact, quotient groups make more sense to me than quotient rings did. I'm not sure why, but it makes a lot of sense to me. However, it makes me wonder two things:
1. What about left cosets? Can groups be defined by G/aN?
2. What if a subgroup K is not normal? Can we say anything about G/K? Is G/K even a group?
Reflective: It is interesting that we can come up with the same results about groups that we did with rings. Groups seem simpler to me, though. I think we can extend a lot of these theorems and ideas to other algebraic systems as well. That must be why research in mathematics continues to deepen!
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment