Geodesic
Finite Factorizable Groups with $\mathbb P$-Subnormal $\mathrm v$-Supersolvable and $\mathrm{sh}$-Supersolvable Factors
Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 403-410 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study a finite factorized group $G=AB$ in the case when the factors $A$ and $B$ can be connected to $G$ by a chain of subgroups with prime indices, and either all subgroups with nilpotent derived subgroups or all Schmidt subgroups in $A$ and $B$ are supersolvable. Such factorizations cover both the groups that are products of normal supersolvable subgroups and mutually permutable products of supersolvable subgroups. In particular, it follows from the results obtained here that all Schmidt subgroups in products of normal supersolvable subgroups and in mutually permutable products of supersolvable subgroups are supersolvable; however, a nonsupersolvable subgroup with nilpotent derived subgroup can exist.
Keywords: finite group, factorized group, Schmidt subgroup.
Mots-clés : supersolvable group 
@article{MZM_2022_111_3_a6,
     author = {V. S. Monakhov},
     title = {Finite {Factorizable} {Groups} with~$\mathbb P${-Subnormal} $\mathrm v${-Supersolvable} and $\mathrm{sh}${-Supersolvable} {Factors}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {403--410},
     year = {2022},
     volume = {111},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a6/}
}
TY  - JOUR
AU  - V. S. Monakhov
TI  - Finite Factorizable Groups with $\mathbb P$-Subnormal $\mathrm v$-Supersolvable and $\mathrm{sh}$-Supersolvable Factors
JO  - Matematičeskie zametki
PY  - 2022
SP  - 403
EP  - 410
VL  - 111
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a6/
LA  - ru
ID  - MZM_2022_111_3_a6
ER  - 
%0 Journal Article
%A V. S. Monakhov
%T Finite Factorizable Groups with $\mathbb P$-Subnormal $\mathrm v$-Supersolvable and $\mathrm{sh}$-Supersolvable Factors
%J Matematičeskie zametki
%D 2022
%P 403-410
%V 111
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a6/
%G ru
%F MZM_2022_111_3_a6
V. S. Monakhov. Finite Factorizable Groups with $\mathbb P$-Subnormal $\mathrm v$-Supersolvable and $\mathrm{sh}$-Supersolvable Factors. Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 403-410. http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a6/

[1] V. S. Monakhov, “O trekh formatsiyakh nad $\mathfrak U$”, Matem. zametki, 110:3 (2021), 358–367 | DOI | Zbl

[2] A. A. Trofimuk, Konechnye faktorizuemye gruppy s ogranicheniyami na somnozhiteli, Izd. tsentr BGU, Minsk, 2021

[3] A. Ballester-Bolinches, R. Estaban-Romero, M. Asaad, Products of Finite Groups, De Gruyter Exp. Math., 53, Walter de Gruyter, Berlin, 2010 | MR | Zbl

[4] The GAP Group: GAP – Groups, Algorithms, and Programming, Ver. 4.11.1 released on 02 March 2021 www.gap-system.org

[5] B. Huppert, Endliche Gruppen. I, Springer-Verlag, Berlin, 1967 | MR | Zbl

[6] A. F. Vasilev, T. I. Vasileva, V. N. Tyutyanov, “O proizvedeniyakh $\mathbb P$-subnormalnykh podgrupp v konechnykh gruppakh”, Sib. matem. zhurn., 53:1 (2012), 59–67 | MR

[7] A. F. Vasilev, “Novye svoistva konechnykh dinilpotentnykh grupp”, Vestn. NAN Belarusi. Ser. fiz.-matem. nauk, 2004, no. 2, 29–33

[8] L. A. Shemetkov, Formatsii konechnykh grupp, Sovremennaya algebra, Nauka, M., 1978 | MR | Zbl