Algebra - Math 320 -- Fall 2009

Prove Theorem 14.1 by doing the following steps. (This proof is not any shorter than the book's. It looks different, but is essentially the same. I want you to do it to practice proving a function is well-defined.)

Define a function f from G to A x B as follows:
For every g in G, pick a in A and b in B such that g = ab; then let f(g) = (a,b).

1. We need to show f is well-defined; explain why (i.e., why isn't it obvious that f is well-defined?).
2. Show f is well-defined.
3. Show f is an isomorphism.