Permutation group

A permutation group is a mathematical way to describe all the ways you can rearrange a set of objects without losing or adding any elements. Imagine shuffling a deck of cards—each different shuffle is a permutation. The permutation group includes all such rearrangements that follow specific rules: combining two shuffles results in another valid shuffle, and there's an "identity" shuffle that leaves everything in place. These groups help us understand symmetry and structure in math and science, providing a framework for analyzing how objects can be systematically transformed while maintaining their core properties.