On an open problem about π-quasi-𝔉-groups
Zhang, Chi1 ; Zhang, Li2 ; Huang, Jianhong3
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.

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 :
DOI : 10.4171/RSMUP/139-6
Classification : 20, 00
Mots-clés : Finite groups, p-quasinilpotent group, fitting formation, p-quasi-F-group, \linebreak π-quasi-F-group
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 = {https://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. https://www.numdam.org/articles/10.4171/RSMUP/139-6/

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