p-超可解融合系

p-supersolvable fusion systems

本文研究有限群.设p是一个素数,S是一个p-群,F为S上的饱和融合系.本文首先给出p-超可解融合系的定义.随后证明p-超可解融合系的模型是p-超可解群,并给出p-超可解融合系的正规子系和因子系的超可解性.最后给出p-超可解融合系的判定准则.

In this paper,we consider finite groups.Let p be a prime and S be a p-group.Let F be a saturated fusion system over S.We first define p-supersolvable fusion systems.Then we prove that the models of psupersolvable fusion systems are p-supersolvable groups and give the p-supersolvablity of normal subsystems and factors of a p-supersolvable fusion system.Last,we give the criterion of p-supersolvable fusion systems.