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

Hu, Bin; Huang, Jianhong; Skiba, Alexander N.

doi:10.4171/rsmup/102

Finite groups with

H_{ℒ}

-embedded subgroups

Hu, Bin ; Huang, Jianhong ; Skiba, Alexander N.

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

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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 = {Hu, Bin and Huang, Jianhong and Skiba, Alexander N.},
     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://archive.numdam.org/articles/10.4171/rsmup/102/}
}

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Hu, Bin; Huang, Jianhong; Skiba, Alexander N. 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://archive.numdam.org/articles/10.4171/rsmup/102/

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