In mathematics, the Brauer–Suzuki theorem, proved by , , , states that if a finite group has a generalized quaternion Sylow 2-subgroup and no non-trivial normal subgroups of odd order, then the group has a center of order 2.
The Brauer–Suzuki theorem, attributed to , , , states that for a finite group containing a generalized quaternion Sylow 2-subgroup and no non-trivial normal subgroups of odd order, the presence of such a subgroup implies the existence of a center with an order of 2.