Cyclic non--permutable subgroups and non-normal maximal subgroups
Gholamreza R. RezaeezadehShahrekord University, Iran
Zahra AghajariShahrekord University, Iran
A finite group is said to be a -group (resp. -group, -group) if normality (resp. permutability, -permutability) is a transitive relation. Ballester-Bolinches et al. gave some new characterizations of the soluble -, - and -groups. A finite group is called a -group (resp. -group, -group) if each cyclic subnormal subgroup is normal (resp. permutable, -permutable) in . The present work defines the -, -, and -groups and presents new characterizations of the wider classes of soluble -, -, and -groups.
Cite this article
Gholamreza R. Rezaeezadeh, Zahra Aghajari, Cyclic non--permutable subgroups and non-normal maximal subgroups. Rend. Sem. Mat. Univ. Padova 137 (2017), pp. 93–100DOI 10.4171/RSMUP/137-5