Directions.
- Get the template for this assignment (or use your own). Here’s how to do it:
- Go to www.overleaf.com, and make sure you are logged in.
- In a new window, go here: https://www.overleaf.com/read/jbzypwgftrgx#35214d
- Click on the menu icon in the upper-left and select “Copy Project”.
- Enter a name and click “Copy”.
- When this completes you will be back in your own workspace (instead of mine).
- Use $\LaTeX$ to type up your proofs of the Propositions to Prove listed below. Make sure to use complete sentences and appropriate punctuation. Also, make sure to edit for typos.
- Click on the “Download PDF” button (to the right of the “Recompile” button). Save the file somewhere you can easily find it. Submit the pdf in Canvas.
- Let me know if you have any questions!
Remember, if you have trouble finding the command for a math symbol you want to use, try googling it, email me, or try looking in this Short Math Guide for $\LaTeX{}$.
Propositions to Prove.
- Prove that if $G$ is a group, then $Z(G)$ is a subgroup of $G$.
- Notes. See Theorem 3.23. I’m only asking you to prove that $Z(G)$ is a subgroup; you don’t need to prove that it’s abelian like was asked in Theorem 3.23.