Cyclic non-SS-permutable subgroups and non-normal maximal subgroups

  • Gholamreza R. Rezaeezadeh

    Shahrekord University, Iran
  • Zahra Aghajari

    Shahrekord University, Iran

Abstract

A finite group GG is said to be a TT-group (resp. PTPT-group, PSTPST-group) if normality (resp. permutability, SS-permutability) is a transitive relation. Ballester-Bolinches et al. gave some new characterizations of the soluble TT-, PTPT- and PSTPST-groups. A finite group GG is called a TcT_c-group (resp. PTc{PT}_c-group, PSTc{PST}_c-group) if each cyclic subnormal subgroup is normal (resp. permutable, SS-permutable) in GG. The present work defines the NNMc{NNM}_c-, PNMc{PNM}_c-, and SNMc{SNM}_c-groups and presents new characterizations of the wider classes of soluble TcT_c-, PTc{PT}_c-, and PSTc{PST}_c-groups.

Cite this article

Gholamreza R. Rezaeezadeh, Zahra Aghajari, Cyclic non-SS-permutable subgroups and non-normal maximal subgroups. Rend. Sem. Mat. Univ. Padova 137 (2017), pp. 93–100

DOI 10.4171/RSMUP/137-5