Geodesic
Products of $\mathrm{F}^*(G)$-subnormal subgroups of finite groups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2017), pp. 76-82

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A subgroup $H$ of a finite group $G$ is called $\mathrm{F}^*(G)$-subnormal if $H$ is subnormal in $H\mathrm{F}^*(G)$. We show that if a group $G$ is a product of two $\mathrm{F}^*(G)$-subnormal quasinilpotent subgroups, then $G$ is quasinilpotent. We also study groups $G=AB$, where $A$ is a nilpotent $\mathrm{F}^*(G)$-subnormal subgroup and $B$ is a $\mathrm{F}^*(G)$-subnormal supersoluble subgroup. Particularly, we show that such groups $G$ are soluble.
Keywords: finite group, $\mathrm{F}^*(G)$-subnormal subgroup, nilpotent group, supersoluble group, product of subgroups.
Mots-clés : quasinilpotent group 
@article{IVM_2017_6_a8,
     author = {V. I. Murashka},
     title = {Products of $\mathrm{F}^*(G)$-subnormal subgroups of finite groups},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {76--82},
     publisher = {mathdoc},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_6_a8/}
}
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V. I. Murashka. Products of $\mathrm{F}^*(G)$-subnormal subgroups of finite groups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2017), pp. 76-82. http://geodesic.mathdoc.fr/item/IVM_2017_6_a8/