Criteria for supersolvability of saturated fusion systems.

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 = S 0 ≤ S 1 ≤ ... ≤ S m = S of subgroups of S such that S i is strongly F -closed for all 0 ≤ i ≤ m and such that S i + 1 / S i 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]. [ABSTRACT FROM AUTHOR]