Read: Section 5.2. Also consider watching the following Socratica video:
Turn in: 5.17, 5.19, 5.20, 5.21, 5.24
- Please try 5.16, even though I’m not asking you to turn it in. We’ll work through it in class together. Consider using 5.11 and 5.13.
- For 5.17, use 5.16.
- For 5.19, think back to the definition of the order of an element, which is about the order of a subgroup.
- On 5.21, see if you can first use Lagrange’s theorem to prove that Theorem 4.10 applies to $G$. Once you know $G$ is cyclic, then you can use Theorem 4.40 to finish up.
- For 5.24, you are being asked to determine only the number of cosets of a subgroup $H$ in a group $G$. You do not need to actually write out the cosets, so you can just use the version of Lagrange’s theorem that says: $| G | = [G:H]\cdot |H|$.