finite group

A finite group is a mathematical structure consisting of a set of elements combined with an operation (like addition or multiplication) that satisfies four key properties: closure (combining any two elements produces another element in the set), associativity (the order of grouping operations doesn't matter), identity (there’s a special element that doesn’t change others when combined), and inverses (each element has a partner that cancels it out). The "finite" part means the set contains a limited number of elements. Finite groups are fundamental in understanding symmetry and structure across mathematics and physics.