Geodesic
New Characterizations of Some Classes of Finite Groups
Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 3 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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Let $G$ be a finite group and $\frak{F}$ a formation of finite groups. We say that a subgroup $H$ of $G$ is $\mathfrak{F}_h$-normal in $G$ if there exists a normal subgroup $T$ of $G$ such that $HT$ is a normal Hall subgroup of $G$ and $(H\cap T)H_G/H_G$ is contained in the $\frak{F}$-hypercenter $Z_\infty ^\frak{F} (G/H_G)$ of $G/H_G$. In this paper, we obtain some results about the $\mathfrak{F}_h$-normal subgroups and use them to study the structure of finite groups. Some new characterizations of supersoluble groups, soluble groups and $p$-nilpotent groups are obtained and some known results are generalized.
Classification : 20D10, 20D15, 20D20. 
@article{BMMS_2011_34_3_a14,
     author = {Wenbin Guo and Xiuxian Feng and Jianhong Huang},
     title = {New {Characterizations} of {Some} {Classes} of {Finite} {Groups}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2011},
     volume = {34},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2011_34_3_a14/}
}
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Wenbin Guo; Xiuxian Feng; Jianhong Huang. New Characterizations of Some Classes of Finite Groups. Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2011_34_3_a14/