10 22 Through 10 29 Feedback
• There are typos in the proof of Theorem 11.16 on lines 3,4, and 5. Also you should use [[$\times$]] for $\times$ instead of $x$
• HW9 Problem 4 (b) is incorrect. See Theorem 11.16 and Theorem 10.10
• HW9 Problem 6, say that you are choosing $(a,b,c)$ of order 3 on line 6. It also would be useful to link to the theorems being used. Careful, $|b|=3$ also when $b=2$; which subgroups contain this case?
• HW8 Problem 1: it’s unnecessary to compute $aH$ for every element $a\in G$, since we know if $a$ and $b$ are in the same coset, then $aH=bH$.
• HW10 Problem 8: The proof is difficult to follow, because many details are left out. For example, why is $\phi(0)=\phi(1)^n$? How is $\langle h \rangle \simeq \mathbb{Z}_m$ and how is the division algorithm being used in the backwards direction? These details need filled in.
• inner automorphism has been defined twice (it’s also under conjugation) We only need one – if you want both words in the glossary, link inner automorphism to the conjugation page. Similarly, you could link conjugate subgroup to the conjugate page and put the definition there.
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