Bm$p$-supersolvable fusion systems

Abstract

In this paper, we consider finite groups. Let $p$ be a prime and $S$ be a $p$-group. Let $\mathcal~{F}$ be a saturatedfusion system over $S$. We first define $p$-supersolvable fusion systems. Then we prove that the models of $p$-supersolvablefusion systems are $p$-supersolvable groups and give the $p$-supersolvablity of normal subsystems and factors of a $p$-supersolvable fusion system. Last, wegive the criterion of $p$-supersolvable fusion systems.