permutation group

A permutation group is a mathematical group whose elements are permutations. A permutation is an arrangement of objects in a specific order. In a permutation group, when you combine two permutations, the result is another permutation that has the same effect as applying the first two in succession.1

The concept of groups, including permutation groups, originated in the 18th and 19th centuries with studies in the theory of equations. Évariste Galois was instrumental in developing this theory, linking it to the permutations of the roots of equations. Group theory is now a fundamental part of abstract algebra and has applications in various fields like geometry, physics, and chemistry.234