Feit–Thompson Theorem

The Feit–Thompson Theorem states that every finite group where all elements have orders (or sizes) that are powers of odd numbers must be a solvable group. In simpler terms, it means that if a mathematical structure (called a finite group) only contains elements with specific mathematical properties related to odd numbers, then this structure can be broken down into simpler, understandable parts. This theorem was a major breakthrough in group theory, helping mathematicians classify and understand all finite groups by showing that certain complex groups are actually built from simpler pieces.