On non-normal cyclic subgroups of prime order or order 4 of finite groups
In this paper, we call a finite group GG an NLMNLM-group (NCMNCM-group, respectively) if every non-normal cyclic subgroup of prime order or order 4 (prime power order, respectively) in GG is contained in a non-normal maximal subgroup of GG. Using the property of NLMNLM-groups and NCMNCM-groups, we g...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2021
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/93bfaa4ff88f45be96cf359eed29f607 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: | In this paper, we call a finite group GG an NLMNLM-group (NCMNCM-group, respectively) if every non-normal cyclic subgroup of prime order or order 4 (prime power order, respectively) in GG is contained in a non-normal maximal subgroup of GG. Using the property of NLMNLM-groups and NCMNCM-groups, we give a new necessary and sufficient condition for GG to be a solvable TT-group (normality is a transitive relation), some sufficient conditions for GG to be supersolvable, and the classification of those groups whose all proper subgroups are NLMNLM-groups. |
|---|