Geodesic
On one-generated and bounded totally $\omega$-composition formations of finite groups
Problemy fiziki, matematiki i tehniki, no. 4 (2021), pp. 101-107

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

All considered groups are finite. Let $G$ be a group. Then $c_{\infty}^\omega\mathrm{form}(G)$ denotes the intersection of all totally $\omega$-composition formations containing $G$. The formation $c_{\infty}^\omega\mathrm{form}(G)$ is called a totally $\omega$-composition formation generated by $G$ or a one-generated totally $\omega$-composition formation. A totally $\omega$-composition formation $\mathfrak{F}$ is called a bounded, if $\mathfrak{F}$ is a subformation of some one-generated totally $\omega$-composition formation, that is, $\mathfrak{F}\subseteq c_{\infty}^\omega\mathrm{form}(G)$ for some group $G$. In this paper, criteria for the one-generation (boundedness) of a totally $\omega$-composition formation are obtained.
Keywords: formation of finite groups, one-generated formation, bounded formation, totally $\omega$-composition formation.
Mots-clés : $\omega$-composition formation 
@article{PFMT_2021_4_a16,
     author = {I. P. Los and V. G. Safonov},
     title = {On one-generated and bounded totally $\omega$-composition formations of finite groups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {101--107},
     publisher = {mathdoc},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2021_4_a16/}
}
TY  - JOUR
AU  - I. P. Los
AU  - V. G. Safonov
TI  - On one-generated and bounded totally $\omega$-composition formations of finite groups
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2021
SP  - 101
EP  - 107
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2021_4_a16/
LA  - ru
ID  - PFMT_2021_4_a16
ER  - 
%0 Journal Article
%A I. P. Los
%A V. G. Safonov
%T On one-generated and bounded totally $\omega$-composition formations of finite groups
%J Problemy fiziki, matematiki i tehniki
%D 2021
%P 101-107
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2021_4_a16/
%G ru
%F PFMT_2021_4_a16
I. P. Los; V. G. Safonov. On one-generated and bounded totally $\omega$-composition formations of finite groups. Problemy fiziki, matematiki i tehniki, no. 4 (2021), pp. 101-107. http://geodesic.mathdoc.fr/item/PFMT_2021_4_a16/