Visual Group Theory, Lecture 3.3: Normal subgroups

Visual Group Theory, Lecture 3.3: Normal subgroups

A subgroup H of G is normal if every left coset gH equals the right coset Hg. In this lecture, we see several different ways of visualizing this concept as well as several equivalent definitions. We conclude with three useful but different ways to check whether a subgroup is normal. In many cases, one of these will be much easier than the other two.

[irplans]

This was the first video in the series that i had to watch twice to completely understand and be able to do the HWs that means we are geting closer to serious stuff😂

[dof]

Are solutions to all the home work for this video and/or Nathan's book on VGT available anywhere?

[MrHowbout]

Great video! I just started watching here though, is D_3 the set of permutations on a set of 3 elements?

[davidkwon]

If G has a unique subgroup of size |H|, then H must be normal (why?)
because gHg-1 is always a subgroup of G so that gHg-1 = H.
By (2), H is normal.