H is a subgroup of G iff H is a sunset of G and H satisfies all the axioms of a group using the multiplication rule of G.

Theorems about subgroups:

- If H and K are subgroups of G then H intersect K is a subgroup of G.
- If H is a subgroup of G and N is a normal subgroup of G, then H
- intersect N is a normal subgroup of H.
- If H is a subgroup of G and N is a normal subgroup of G, then NH=HN
- is a subgroup of G, not necesserily normal.
- If H and N are both normal subgroups of G, then H intersect N, and
- HN are both normal subgroups of G.

source

jl@crush.caltech.edu index

semi_direct_product

commutator_subgroup

group_generation

symmetric_group

normal_subgroup

point_group

generator

simple

group

coset

SL

GL

An