Homework 9 - Normal Subgroups and Quotient Groups
Due Date: May 1, 2023
Be sure to show enough work on how you arrived at your answers. When it doubt, it is best to show more work than to show none at all. Problems taken from Chapter 10 - Normal Subgroups and Factor Groups.
Problems
- Problem 3: Recall that if \(G\) is a group then \(G\) and \(\{e\}\) are subgroups of \(G\). See one of the examples in Section 3.2 for the definition of the quaternion group.
- Problem 12: Hint: Show that \(y\, C(g)y^{-1} \subset C(g)\) for all \(y\in G\).
- Problem 13