Permutation Groups
A permutation group is a mathematical concept in group theory that consists of a set of permutations of a given set, along with the operation of composition. Each permutation is a rearrangement of the elements in the set, and the group structure allows for the combination of these rearrangements. The identity permutation, which leaves all elements unchanged, is always included in the group.
Permutation groups are often studied in the context of symmetric groups, which contain all possible permutations of a finite set. They play a crucial role in various areas of mathematics, including combinatorics, algebra, and geometry, as they help in understanding the symmetries and structures of mathematical objects.