Groups (of elements)

A group is a mathematical concept related to sets of elements that can be combined using a specific operation, like addition or multiplication. It must satisfy four rules: you can combine any two elements to get another element in the set (closure); the operation has an identity element that leaves others unchanged; each element has an inverse that reverses its effect; and the operation is associative, meaning the order of grouping does not matter. Groups help us understand symmetry, structure, and patterns in various fields, from mathematics and physics to computer science.