301.9B Normal Subgroups: Motivation and Definition

A subgroup H in G is normal if its cosets themselves form a group. In this video we see what it looks like when this requirement is *not* satisfied, then determine a definition that will guarantee that it *is*, and look at two consequences of that definition.

[AdrianYang]

Thank you so much for connecting congruence relations with quotient groups. I found in many places of group theory, it is about how to preserve the structure: e.g. homomorphism and congruence relation. I never learned any more advanced algebra than linear algebra in university, but it is amazing to know that a map can act on not only operands, but also operators.

[dairahheinz]

At 2:31, in the N table, more than one coset has the element (1423). Namely, (12)N and (14)N.

[PunmasterSTP]

Normal subgroups? More like "Nice lectures that help us jump through hoops!" 👍⭕

[maurocruz]

14:40 It happens because cosets are a partition of the larger group.