Math History | NJ Wildberger

Summary:

- Normal subgroup
- Quotient Group
- Finite Simple Group: Z5, D5,…
- Tesselation (regular)
- Platonic solids

… Two families of Group :

- Symmetric Groups: Sn
- Linear Group: GL(n) = M, det M ≠0

…

An = Alternating Group

[even permutation, det = +1]

n>=5, An is a Simple (non-commutative) Group

**Lie Groups :**

SO(2)

SO(3)

Simple Lie Groups : Matrix Group M

- Special Linear Group: SL(n), det M = 1
- Orthogonal Group: O(n), $latex M. M^T = I$
- Symplectic Group : Sp(2n)

…