Relevant Courses: Math 493 Resources Used: https://youtu.be/wE1kxAChirg?si=jqv2ogzeMJQiZOw6
The Jordan-Hölder Theorem
Suppose the group has a composition series. Then:
a. All composition series have the same length. b. The successive quotients (called the Jordan-Hölder factors) are are the same (isomorphic) up to reordering.
Proof: