On the intersection of non-normal maximal subgroups of a finite group

  • Zahra Aghajari

    Shahrekord University, Iran
  • Gholamreza Rezaeezadeh

    Shahrekord University, Iran
On the intersection of non-normal maximal subgroups of a finite group cover
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Abstract

The subgroup of a group is defined to be the intersection of all non-normal maximal subgroups of (and if all maximal subgroups of G are normal). A group is called a -group if is a -group. Ballester-Bolinches et al. [3] considered the class of -groups and gave several results of such groups. In particular, they showed if is a solvable group, the classes of -groups and -groups (that is, a group in which is a -group) are equal. The present work, we introduce the class of -groups which are defined as the groups for which is an -group and we show several results of the class -groups. Also, we discuss about equivalency the classes of solvable -groups and solvable -groups.

Cite this article

Zahra Aghajari, Gholamreza Rezaeezadeh, On the intersection of non-normal maximal subgroups of a finite group. Rend. Sem. Mat. Univ. Padova 142 (2019), pp. 135–143

DOI 10.4171/RSMUP/34