A finite group is a mathematical structure consisting of a set of elements combined with an operation that satisfies four key properties: closure, associativity, identity, and invertibility. The set has a limited number of elements, meaning it contains a finite number of members. Finite groups are essential in various areas of mathematics, including group theory and abstract algebra. One common example of a finite group is the set of integers modulo n, denoted as Z/nZ, where n is a positive integer. In this group, the operation is addition modulo n, and it contains exactly n elements. Finite groups are crucial for understanding symmetry, permutations, and many other mathematical concepts.