Unit · year 2
MU-204 · Group Theory
Threads structure6 theorems
The mathematics of symmetry, from Lagrange's theorem to the Sylow theorems.
Theorems in this unit
T-057
Lagrange's theorem
The order of a subgroup divides the order of the group.
T-058
The orbit–stabiliser theorem
Orbit size times stabiliser size equals the group order.
T-059
The first isomorphism theorem
The image of a homomorphism is the quotient by its kernel.
T-060
Cauchy's theorem
If a prime divides the group order, an element of that order exists.
T-061
The Sylow theorems
Existence, conjugacy, and counting of maximal p-subgroups.
T-062
Structure of finite abelian groups
Every finite abelian group is a product of cyclic groups.