Geodesic
On the Kegel--Wielandt $\sigma$-Problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 121-129

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

For an arbitrary partition $\sigma$ of the set $\mathbb{P}$ of all primes, a sufficient condition for the $\sigma$-subnormality of a subgroup of a finite group is given. It is proved that the Kegel–Wielandt $\sigma$-problem has a positive solution in the class of all finite groups all of whose nonabelian composition factors are alternating groups, sporadic groups, or Lie groups of rank $1$.
Keywords: finite group, $\sigma$-subnormal subgroup, Kegel–Wielandt $\sigma$-problem, Hall subgroup, complete Hall set. 
@article{TIMM_2023_29_4_a9,
     author = {S. F. Kamornikov and V. N. Tyutyanov},
     title = {On the {Kegel--Wielandt} $\sigma${-Problem}},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {121--129},
     publisher = {mathdoc},
     volume = {29},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a9/}
}
TY  - JOUR
AU  - S. F. Kamornikov
AU  - V. N. Tyutyanov
TI  - On the Kegel--Wielandt $\sigma$-Problem
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2023
SP  - 121
EP  - 129
VL  - 29
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a9/
LA  - ru
ID  - TIMM_2023_29_4_a9
ER  - 
%0 Journal Article
%A S. F. Kamornikov
%A V. N. Tyutyanov
%T On the Kegel--Wielandt $\sigma$-Problem
%J Trudy Instituta matematiki i mehaniki
%D 2023
%P 121-129
%V 29
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a9/
%G ru
%F TIMM_2023_29_4_a9
S. F. Kamornikov; V. N. Tyutyanov. On the Kegel--Wielandt $\sigma$-Problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 121-129. http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a9/