Criteria for supersolvability of saturated fusion systems

Abstract

Let p be a prime number. A saturated fusion system F on a finite p-group S is said to be supersolvable if there is a series 1=S0≤S1≤…≤Sm=S of subgroups of S such that Si is strongly F-closed for all 0≤i≤m and such that Si+1/Si is cyclic for all 0≤i<m. We prove some criteria that ensure that a saturated fusion system F on a finite p-group S is supersolvable provided that certain subgroups of S are abelian and weakly F-closed. Our results can be regarded as generalizations of purely group-theoretic results of Asaad [3].