Read: Continue with Section 3.3.
Turn in: 3.51, 3.54, 3.56, 3.61
- For 3.51, you are given a function and need to check three things: (1) does it satisfy the homomorphic property in Definition 3.48, (2) is it one-to-one, and (3) is it onto. If any one of them fails, it is not an isomorphism.
- There are multiple ways to approach 3.54. If you want a hint: one approach is to start by applying \(\phi\) to both sides of the equation \(e_1 = g*g^{-1}\).
- For 3.56 you can use (without proof) that the composition of two bijections is a bijection. So the main thing is to prove that if \(\phi\) and \(\psi\) both satisfy the homomorphic property, then the composition \(\psi\circ\phi\) does too.