If a Sylow p-subgroup of a finite group is a generalized extraspecial group, then its normalizer controls p-fusion, except in a small case. This can be generalized to Brauer pairs associated to a block whose defect group is a generalized extraspecial group. Even more generally, this holds for Frobenius systems over a generalizer extraspecial p-group. Other results can be proved for Frobenius systems over a p-group, such as the Gilotti-Serena criterion for control of fusion.