simple groups

Simple groups are fundamental building blocks in the study of symmetry in mathematics. Think of them as the most basic groups that cannot be broken down into smaller, non-trivial symmetry groups through a process called "composition." They serve as the basic units from which all other groups can be constructed or understood, much like prime numbers are the basic units of multiplication. The classification of all finite simple groups was a major achievement in mathematics, providing a comprehensive understanding of symmetry structures in various mathematical and scientific contexts.