On an open problem about $\pi$-quasi-$\mathfrak{F}$-groups

Zhang, Chi; Zhang, Li; Huang, Jianhong

doi:10.4171/RSMUP/139-6

On an open problem about

π

-quasi-

𝔉

-groups

Zhang, Chi ¹ ; Zhang, Li ² ; Huang, Jianhong ³

¹ University of Science and Technology of China, Hefei, Anhui, China
² Anhui Jianzhu University, Hefei, Anhui, China
³ Jiangsu Normal University, Xuzhou, Jiangsu, China

Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 185-194.

Résumé

Let $𝔉$ be a class of finite groups, $p$ a prime and $π$ a set of some primes. A finite group $G$ is called a $p$ -quasi- $𝔉$ -group (respectively, by $π$ -quasi- $𝔉$ -group) provided that for every $𝔉$ -eccentric $G$ -chief factor $H / K$ of order divisible by $p$ (respectively, by at least one prime in $π$ ), the automorphisms of $H / K$ induced by all elements of $G$ are inner. In this paper, we obtain the characterizations of $p$ -quasi- $𝔉$ -groups and $π$ -quasi- $𝔉$ -groups, which give a positive answer to an open problem in the book [3].

Publié le : 2018-06-06

MR Zbl

DOI : 10.4171/RSMUP/139-6

Classification : 20, 00
Mots-clés : Finite groups, $p$-quasinilpotent group, fitting formation, $p$-quasi-$\mathfrak{F}$-group, \linebreak $\pi$-quasi-$\mathfrak{F}$-group

Affiliations des auteurs :

Zhang, Chi ¹ ; Zhang, Li ² ; Huang, Jianhong ³

¹ University of Science and Technology of China, Hefei, Anhui, China
² Anhui Jianzhu University, Hefei, Anhui, China
³ Jiangsu Normal University, Xuzhou, Jiangsu, China

@article{RSMUP_2018__139__185_0,
     author = {Zhang, Chi and Zhang, Li and Huang, Jianhong},
     title = {On an open problem about $\pi$-quasi-$\mathfrak{F}$-groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {185--194},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {139},
     year = {2018},
     doi = {10.4171/RSMUP/139-6},
     mrnumber = {3825185},
     zbl = {1396.20012},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/139-6/}
}

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Zhang, Chi; Zhang, Li; Huang, Jianhong. On an open problem about $\pi$-quasi-$\mathfrak{F}$-groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 185-194. doi : 10.4171/RSMUP/139-6. http://www.numdam.org/articles/10.4171/RSMUP/139-6/

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