alternating group

The alternating group is a mathematical concept that involves permutations, or arrangements, of a set of objects. Specifically, it includes all the even permutations—those that can be achieved by swapping objects in pairs an even number of times. For example, if you have a set of items, the alternating group consists of those arrangements obtained without changing the overall order too drastically. In essence, it captures the structure of "nice" rearrangements that preserve certain symmetries, playing a key role in group theory and symmetry studies across mathematics and physics.