Finite Group with Two Supersolvable Subgroups of Coprime Indices

摘要

In this paper, we obtain some classification theorems of finite simple groups with two subgroups of coprime indices which are both super solvable or one super solvable and the other nilpotent. Using these classification theorems, we prove some sufficient conditions of finite solvable groups. Finally, we provide a supplement of Doerk's Theorem.