Finite groups with $H_{\mathcal L}$-embedded subgroups

Bin Hu; Jianhong Huang; Alexander N. Skiba

doi:10.4171/rsmup/102

Finite groups with

H_{ℒ}

-embedded subgroups

Bin Hu ; Jianhong Huang ; Alexander N. Skiba

Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 51-63.

Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez l'article sur le site de la revue.

Résumé

Let $G$ be a finite soluble group and let $𝔉$ be a class of groups. A chief factor $H / K$ of $G$ is said to be $𝔉$ -central (in $G$ ) if $(H / K) ⋊ (G / C_{G} (H / K)) \in 𝔉$ ; we write $ℒ_{c 𝔉} (G)$ to denote the set of all subgroups $A$ of $G$ such that every chief factor $H / K$ of $G$ between $A_{G}$ and $A^{G}$ is $𝔉$ -central in $G$ . Let $ℒ$ be a set of subgroups of $G$ . We say that a subgroup $A$ of $G$ is $H_{ℒ}$ -embedded in $G$ provided $A$ is a Hall subgroup of some subgroup $E \in ℒ$ . In this paper, we study the structure of $G$ under the condition that every subgroup of $G$ is $H_{ℒ}$ -embedded in $G$ , where $ℒ = ℒ_{c 𝔉} (G)$ for some hereditary saturated formation $𝔉$ . Some known results are generalized.

Accepté le : 2020-09-07
Publié le : 2022-12-01

DOI : 10.4171/rsmup/102

Classification : 20

@article{RSMUP_2022__148__51_0,
     author = {Bin Hu and Jianhong Huang and Alexander N. Skiba},
     title = {Finite groups with $H_{\mathcal L}$-embedded subgroups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {51--63},
     volume = {148},
     year = {2022},
     doi = {10.4171/rsmup/102},
     mrnumber = {4542372},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/102/}
}

TY  - JOUR
AU  - Bin Hu
AU  - Jianhong Huang
AU  - Alexander N. Skiba
TI  - Finite groups with $H_{\mathcal L}$-embedded subgroups
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2022
SP  - 51
EP  - 63
VL  - 148
UR  - http://www.numdam.org/articles/10.4171/rsmup/102/
DO  - 10.4171/rsmup/102
LA  - en
ID  - RSMUP_2022__148__51_0
ER  -

%0 Journal Article
%A Bin Hu
%A Jianhong Huang
%A Alexander N. Skiba
%T Finite groups with $H_{\mathcal L}$-embedded subgroups
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2022
%P 51-63
%V 148
%U http://www.numdam.org/articles/10.4171/rsmup/102/
%R 10.4171/rsmup/102
%G en
%F RSMUP_2022__148__51_0

Bin Hu; Jianhong Huang; Alexander N. Skiba. Finite groups with $H_{\mathcal L}$-embedded subgroups. Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 51-63. doi : 10.4171/rsmup/102. http://www.numdam.org/articles/10.4171/rsmup/102/

Cité par Sources :