Center, Centralizer and Normalizer (Algebra 1: Lecture 3 Video 2)

Lecture 3: In Lecture 3, we started by discussing properties of homomorphisms and explaining how the kernel of a homomorphism gives a subgroup. We then focused on the center of a group and the centralizer and normalizer of a subset in a group. We defined what it means for a subgroup to be normal. In the last video, we focused on the 'product set' arising from two subgroups HK.

Reading: The first result we talked about was Proposition 1 in Section 3.1. We will talk about the rest of Section 3.1 in the next lecture. It would now be helpful to read Section 1.6, which contains some key examples of Homomorphisms and Isomorphisms. We then moved to Section 2.2 where we covered everything except the section at the end on 'Stabilizers and Kernels of Group Actions' (you can skip this for now). In the last video we discussed Proposition 14 and Corollary 15 in Section 3.2. We will cover the rest of Section 3.2 in the next two lectures.