Geodesic
Finite groups with given Schmidt subgroups
Problemy fiziki, matematiki i tehniki, no. 1 (2022), pp. 84-88

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

Throughout the article, all groups are finite and $G$ always denotes a finite group. A subgroup $H$ of the group $G$ is called $\mathfrak{U}_p$-normal in $G$ ($p$ is a prime) if every chief factor of the group $G$ between $H^G$ and $H_G$ is either cyclic or a $p'$-group. In this article, we prove that if each Schmidt subgroup of the group $G$ is either subnormal or $\mathfrak{U}_p$-normal in $G$, then the derived subgroup $G'$ of $G$ is $p$-nilpotent. Some well-known results are generalized.
Keywords: finite group, nilpotent group, subnormal subgroup, $\mathfrak{U}_p$-normal subgroup, Schmidt group. 
@article{PFMT_2022_1_a12,
     author = {V. M. Sel'kin and V. S. Zakrevskaya and N. S. Kosenok},
     title = {Finite groups with given {Schmidt} subgroups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {84--88},
     publisher = {mathdoc},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2022_1_a12/}
}
TY  - JOUR
AU  - V. M. Sel'kin
AU  - V. S. Zakrevskaya
AU  - N. S. Kosenok
TI  - Finite groups with given Schmidt subgroups
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2022
SP  - 84
EP  - 88
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2022_1_a12/
LA  - ru
ID  - PFMT_2022_1_a12
ER  - 
%0 Journal Article
%A V. M. Sel'kin
%A V. S. Zakrevskaya
%A N. S. Kosenok
%T Finite groups with given Schmidt subgroups
%J Problemy fiziki, matematiki i tehniki
%D 2022
%P 84-88
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2022_1_a12/
%G ru
%F PFMT_2022_1_a12
V. M. Sel'kin; V. S. Zakrevskaya; N. S. Kosenok. Finite groups with given Schmidt subgroups. Problemy fiziki, matematiki i tehniki, no. 1 (2022), pp. 84-88. http://geodesic.mathdoc.fr/item/PFMT_2022_1_a12/