Volume 35 • Number 1 • 2012   • The Influence of $CAP^\ast$-Subgroups on the Solvability of Finite Groups Jianjun Liu, Xiuyun Guo and Shirong Li Abstract. A subgroup $H$ of a group $G$ is said to be a $CAP^{\ast}$-subgroup of a group $G$ if, for any non-Frattini chief factor $K/L$ of $G$, we have $HK=HL$ or $H\cap K=H\cap L$. In this paper, some new characterizations for finite solvable groups are obtained based on the assumption that some subgroups are $CAP^{\ast}$-subgroups of $G$. 2010 Mathematics Subject Classification: 20D10, 20D20. Full text: PDF