Saturated fusion systems over a class of finite p-groups

Abstract

Let p be an odd prime and F be a saturated fusion system over a finite p-group S with derived subgroup of prime order, excepting the case when S≅P×A where P is a minimal nonabelian p-group with P′∩℧1(P)=1, ℧1(P) is cyclic, and A is a finite abelian p-group. In this paper, we prove that S⊴F. That is, S is resistant. This generalizes a result of Stancu in the odd prime case.