Geodesic
The Influence of $CAP^\ast$-Subgroups on the Solvability of Finite Groups
Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 1 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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 $G$.
Classification : 20D10, 20D20. 
@article{BMMS_2012_35_1_a20,
     author = {Jianjun Liu and Xiuyun Guo and Shirong Li},
     title = {The {Influence} of $CAP^\ast${-Subgroups} on the {Solvability} of {Finite} {Groups}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2012},
     volume = {35},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2012_35_1_a20/}
}
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Jianjun Liu; Xiuyun Guo; Shirong Li. The Influence of $CAP^\ast$-Subgroups on the Solvability of Finite Groups. Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2012_35_1_a20/