symmetric groups

Symmetric groups are mathematical structures that describe the different ways to arrange a set of items. For example, if you have three distinct objects, the symmetric group corresponding to these objects includes all the possible ways to arrange them—six arrangements in total (like ABC, ACB, BAC, BCA, CAB, CBA). These groups are foundational in fields like algebra and combinatorics, and they help mathematicians understand symmetry and permutations, which are key concepts in various areas of mathematics and science.