Cyclic non-$S$-permutable subgroups and non-normal maximal subgroups

Rezaeezadeh, Gholamreza; Aghajari, Zahra

doi:10.4171/RSMUP/137-5

Cyclic non-

S

-permutable subgroups and non-normal maximal subgroups

Rezaeezadeh, Gholamreza ¹ ; Aghajari, Zahra ¹

¹ Shahrekord University, SHAHREKORD, IRAN

Rendiconti del Seminario Matematico della Università di Padova, Tome 137 (2017), pp. 93-100.

Résumé

A finite group $G$ is said to be a $T$ -group (resp. $P T$ -group, $P S T$ -group) if normality (resp. permutability, $S$ -permutability) is a transitive relation. Ballester-Bolinches et al. gave some new characterizations of the soluble $T$ -, $P T$ - and $P S T$ -groups. A finite group $G$ is called a $T_{c}$ -group (resp. ${P T}_{c}$ -group, ${P S T}_{c}$ -group) if each cyclic subnormal subgroup is normal (resp. permutable, $S$ -permutable) in $G$ . The present work defines the ${N N M}_{c}$ -, ${P N M}_{c}$ -, and ${S N M}_{c}$ -groups and presents new characterizations of the wider classes of soluble $T_{c}$ -, ${P T}_{c}$ -, and ${P S T}_{c}$ -groups.

MR Zbl

DOI : 10.4171/RSMUP/137-5

Classification : 20
Mots clés : Finite groups, permutability, sylow-permutability, maximal subgroups, supersolubility

Affiliations des auteurs :

Rezaeezadeh, Gholamreza ¹ ; Aghajari, Zahra ¹

¹ Shahrekord University, SHAHREKORD, IRAN

@article{RSMUP_2017__137__93_0,
     author = {Rezaeezadeh, Gholamreza and Aghajari, Zahra},
     title = {Cyclic non-$S$-permutable subgroups and non-normal maximal subgroups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {93--100},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {137},
     year = {2017},
     doi = {10.4171/RSMUP/137-5},
     mrnumber = {3652870},
     zbl = {1365.20015},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/137-5/}
}

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%A Aghajari, Zahra
%T Cyclic non-$S$-permutable subgroups and non-normal maximal subgroups
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2017
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%V 137
%I European Mathematical Society Publishing House
%C Zuerich, Switzerland
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Rezaeezadeh, Gholamreza; Aghajari, Zahra. Cyclic non-$S$-permutable subgroups and non-normal maximal subgroups. Rendiconti del Seminario Matematico della Università di Padova, Tome 137 (2017), pp. 93-100. doi : 10.4171/RSMUP/137-5. http://www.numdam.org/articles/10.4171/RSMUP/137-5/

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