Group theory

Group theory studies sets with a special operation that follows certain rules. A group is a set of elements with an operation (like addition or multiplication) that combines any two elements to make another element in the set. The operation must satisfy four rules: closure, associativity, identity, and inverses.

Important properties

• Closure: Combining any two elements gives another element in the set.

• Associativity: The way elements are grouped when combining does not change the result.

• Identity: There is an element that does not change other elements when combined.

• Inverse: Every element has another element that combines with it to give the identity.