In mathematical finite group theory, the Brauer–Fowler theorem, proved by Brauer & Fowler (1955), states that if a group has even order g > 2 then it has a subgroup of order greater than g1/3. This implies that up to isomorphism there are only a finite number of finite groups with a given centralizer of an involution, which suggested that finite simple groups could be classified by studying their centralizers of involutions, a program that was later realized in the classification of finite simple groups.