Let be a Group and a set. A group action is a mapping such that for all we have: (We use convention that means ) An action is equivalent to a Homomorphism with Orbit Transitive Stabilizer Stabilizer of Group Action Orbit-Stabilizer Theorem Conjugacy Class Centralizer Center Normalizer Burnside’s Lemma Category Theory Definition If is a Group, a group action is a Functor to Category of Sets It consists of a set (the singular element of is mapped to ) and mappings where