What is...a (normal) subgroup?

Goal.
Explaining basic concepts of (a classical course in) algebra in an intuitive way.

This time.
What is...a (normal) subgroup? Or: Why care about the difference?

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Slides.

Material used.

Subgroups vs. normal subgroups.

Translation group.

Tetrahedron.

Mathematica.

Pictures.

#algebra
#galoistheory
#mathematics