[catnaroek]

The Sylow theorems are by no means “fancy”. If you don't understand them, then you don't know group theory, plain and simple.

Now, we can debate the merits of exposing children to groups before they can understand group theory. But learning group theory means learning (0) the axiomatic definitions of group, subgroup, coset, etc. (1) the main theorems in group theory and their proofs.

[alexberke]

some of those things are on the book's Theory Reference page, which is linked to be some of the underlined concepts in the book: http://www.coloring-book.co/#!/theory-reference