Normal Subgroup, also called an invariant subgroup:

- Given a group G, a subgroup H is called normal
- <=> the left cosets and the right cosets are the same.
- <=> H contains the complete conjugacy classes of G.
- <=> forall a ~ b, a in H or a notin H.
- <=> H=g^Hg

{e},G are trivially normal

if G has no nontrivial normal subgroups => G is simple

N normal subset of G => G/N (group division) is a group of order n/m

source

jl@crush.caltech.edu index

semi_direct_product

euclidean_group

poincare_group

homomorph

subgroup

kernel

center

group

SU

An