Скачать или смотреть Cosets of Products of Subgroups (Algebra 1: Lecture 6 Video 3)

Lecture 6: In this lecture we focused on the First Isomorphism Theorem and the Second/Diamond Isomorphism Theorem. We saw that under the assumption that A is a subset of N_G(B) the Second Isomorphism Theorem showed that the index of A \cap B in A is equal to the index of B in AB. We saw that this was a special case of a more general result like this that holds when are finitely subgroups, but we do not necessarily have A a subset of N_G(B).

Reading: The Isomorphism Theorems are the subject of Section 3.3. We followed the first part of this section pretty closely, but filled in some additional details in the proofs. We then went back and proved Proposition 13 in Section 3.2. We have now covered all of Section 3.2. We will cover the rest of Section 3.3 in the next lecture.