What are...the Sylow theorems?

Goal. Explaining basic concepts of (a classical course in) algebra in an intuitive way. This time. What are...the Sylow theorems? Or: Canonical substructures? Disclaimer. Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references. Slides. http://www.dtubbenhauer.com/youtube.html Material used. https://www.daniellitt.com/blog/2020/12/26/the-geometry-of-the-sylow-theorems https://en.wikipedia.org/wiki/Sylow_theorems https://mathstrek.blog/2012/10/02/intermediate-group-theory-2/ Group-wiki. https://groupprops.subwiki.org/wiki/Subgroup_structure_of_symmetric_groups #algebra #galoistheory #mathematics