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, established by , , , indicates that if a finite group has a generalized quaternion Sylow 2-subgroup and does not contain any non-trivial normal subgroups of odd order, then it must have a center with an order of 2.