Abstract Algebra. The Orbit-Stabilizer Theorem

Title: Abstract Algebra. The Orbit-Stabilizer Theorem

Abstract: We describe the orbit-stabilizer theorem, and then use it in order to count that there are 24 rotational symmetries of the cube, and to count that there are 60 rotational symmetries of the soccer ball. We end by defining the stabilizer of an element in a set under a group of permutations.