Writing Assignment 03

Directions.

1. Review the Learning $\LaTeX{}$ document. If you have trouble finding the command for a math symbol you want to use, try looking in this Short Math Guide for $\LaTeX{}$.
2. 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/vqtjypdqmmvq
   • Click on the menu icon in the upper-left and select “Copy Project”.
   • When ask for a name, choose something like “Math 210A - WA 03” and click “Copy”.
   • When this completes you will be back in your own workspace (instead of mine).
3. Use $\LaTeX$ to type up your proof(s) of the proposition(s) listed below. Make sure to use complete sentences and appropriate punctuation. Also, make sure to edit for typos.
4. Click on the download pdf button (second one to the right of the “Recompile” button). Save the file somewhere you can easily find it.
5. Submit the pdf in Canvas for the assignment Writing 03.
6. Let me know if you have any questions!

The Proposition to Prove.

Proposition. Let $N$ be a central subgroup of $G$ (meaning that $N\le Z(G)$). If $G/N$ is cyclic, then $G$ is abelian.