Geodesic
Finite Groups with~$\mathfrak F$-Subnormal Subgroups
Matematičeskie zametki, Tome 108 (2020) no. 2, pp. 215-223.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $G$ be a finite group, let $M$ be a maximal subgroup of $G$, and let $\mathfrak F$ be a hereditary formation consisting of solvable groups. The metanilpotency of the $\mathfrak F$-residual $G^\mathfrak F$ is established under the assumption that all subgroups maximal in $M$ are $\mathfrak F$-subnormal in $G$, and the nilpotency of $G^\mathfrak F$ is established in the case where $\mathfrak F$ is saturated. Properties of the group $G$ are indicated in more detail for the formation of all solvable groups with Abelian Sylow subgroups, for the formation of all supersolvable groups, and for the formation of all groups with nilpotent commutator subgroup.
Keywords: finite group, maximal subgroup, subnormal subgroup, residual.
Mots-clés : formation 
@article{MZM_2020_108_2_a5,
     author = {M. N. Konovalova},
     title = {Finite {Groups} with~$\mathfrak F${-Subnormal} {Subgroups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {215--223},
     publisher = {mathdoc},
     volume = {108},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_2_a5/}
}
TY  - JOUR
AU  - M. N. Konovalova
TI  - Finite Groups with~$\mathfrak F$-Subnormal Subgroups
JO  - Matematičeskie zametki
PY  - 2020
SP  - 215
EP  - 223
VL  - 108
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2020_108_2_a5/
LA  - ru
ID  - MZM_2020_108_2_a5
ER  - 
%0 Journal Article
%A M. N. Konovalova
%T Finite Groups with~$\mathfrak F$-Subnormal Subgroups
%J Matematičeskie zametki
%D 2020
%P 215-223
%V 108
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2020_108_2_a5/
%G ru
%F MZM_2020_108_2_a5
M. N. Konovalova. Finite Groups with~$\mathfrak F$-Subnormal Subgroups. Matematičeskie zametki, Tome 108 (2020) no. 2, pp. 215-223. http://geodesic.mathdoc.fr/item/MZM_2020_108_2_a5/

[1] L. A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978 | MR

[2] V. S. Monakhov, Vvedenie v teoriyu konechnykh grupp i ikh klassov, Vysheishaya shkola, Minsk, 2006

[3] V. S. Monakhov, V. N. Kniahina, “Finite groups with $\mathbb P$-subnormal subgroups”, Ric. Mat., 62:2 (2013), 307–322 | DOI | MR | Zbl

[4] V. A. Kovaleva, A. N. Skiba, “Finite soluble groups with all $n$-maximal subgroups $\mathfrak{F}$-subnormal”, J. Group Theory, 17:2 (2014), 273–290 | DOI | MR | Zbl

[5] V. S. Monakhov, “O gruppakh s formatsionno subnormalnymi $2$-maksimalnymi podgruppami”, Matem. zametki, 105:2 (2019), 269–277 | DOI | Zbl

[6] A. Ballester-Bolinches, L. M. Ezquerro, Classes of Finite Groups, Math. Appl. (Springer), 584, Springer, Dordrecht, 2006 | MR | Zbl

[7] G. A. Miller, H. C. Moreno, “Nonabelian groups in which every subgroup is abelian”, Trans. Amer. Math. Soc., 4:4 (1903), 398–404 | DOI | MR | Zbl