Almost All Generalized Extraspecial p-Groups Are Resistant

A p-group P is called resistant if, for any finite group G having P as a Sylow p-subgroup, the normalizer NG(P) controls p-fusion in G. The aim of this paper is to prove that any generalized extraspecial p-group P is resistant, excepting the case when P = E × A, where A is elementary abelian and E is dihedral of order 8 (when p = 2) or extraspecial of order p3 and exponent p (when p is odd). This generalizes a result of Green and Minh.