18 - Cayley Theorem
We did an example to highlight some of the common definitions like Orbit and Stabilizers.
Here are some of the theorems talked about:
The left regular representation of is the Homomorphism (or Group Morphism)
Some Corollaries
If
Proof
Suppose
But all the prime divisors of
☐
Suppose
- This action is always Transitive (Group Action)
- The stabilizer of the identity coset is
. - The Kernel of
is the intersection of all conjugates of . It is the largest Normal Subgroup of contained in .