On the intersection of non-normal maximal subgroups of a finite group
Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 135-143.
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The subgroup Δ(G) of a group G is defined to be the intersection of all non-normal maximal subgroups of G (and Δ(G)=G if all maximal subgroups of G are normal). A group G is called a T 2 -group if G/Δ(G) is a T-group. Ballester-Bolinches et al. [3] considered the class of T 2 -groups and gave several results of such groups. In particular, they showed if G is a solvable group, the classes of T 2 -groups and PST 2 -groups (that is, a group in which G/Δ(G) is a PST-group) are equal. The present work, we introduce the class of SST 2 -groups which are defined as the groups G for which G/Δ(G) is an SST-group and we show several results of the class SST 2 -groups. Also, we discuss about equivalency the classes of solvable PST 2 -groups and solvable SST 2 -groups.

Publié le :
DOI : 10.4171/RSMUP/34
Classification : 20, 00
Mots clés : Maximal subgroups, $PST$-groups, $SST$-groups
Aghajari, Zahra 1 ; Rezaeezadeh, Gholamreza 1

1 Shahrekord University, Iran
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     author = {Aghajari, Zahra and Rezaeezadeh, Gholamreza},
     title = {On the intersection of non-normal maximal subgroups of a finite group},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {135--143},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {142},
     year = {2019},
     doi = {10.4171/RSMUP/34},
     mrnumber = {4032808},
     zbl = {1445.20011},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/34/}
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Aghajari, Zahra; Rezaeezadeh, Gholamreza. On the intersection of non-normal maximal subgroups of a finite group. Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 135-143. doi : 10.4171/RSMUP/34. http://www.numdam.org/articles/10.4171/RSMUP/34/

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