11 1 Through 11 12 Feedback
• HW10 Problem 6(b): We don’t use commas in elements of $S_n$. Why is the map defined a homomorphism? Why is the map in (c) a homomorphism?
• Theorem 15.9 The statement is missing a word (factor group, not factor).
• HW10 Problem 4 The first sentence of the proof is not a complete sentence.
• HW9 Problem 5 Why do (3)-(6) have more than one subgroup of order 3?
• HW10 Problem 3 (b): you’ve shown that $\{(4m, 3m) \mid m \in \mathbb{Z}\}$ is contained in the kernel, but not the other way around.
• HW10 Problem 5: The first sentence of the proof is not a complete sentence.
• HW9 Problem 9 Use complete sentences: Let $(a_1, a_2, \dots, a_n) \in G$ such that $a_i \in \mathbb{Z}_{p_i^{r_{i}}}$. Then … . etc. Also, you’ve used both $r_i$ and $n_i$. Pick one.
• HW11 Problem 10: Why are $H$ and $K$ isomorphic?
• HW12 Problem 7 Why are the characteristics as given?
• HW11 Problem 4 We still need an example that $H\cap N$ need not be normal in $G$.
• HW12 Problem 12 How does $a-1=0$ imply there are no zero divisors?