A class of generalised finite T-groups
Let F be a formation (of finite groups) containing all nilpotent groups such that any normal subgroup of any T-group in F and any subgroup of any soluble T-group in F belongs to F. A subgroup M of a finite group G is said to be F-normal in G if G/CoreG(M) belongs to F. Named after Kegel, a subgroup...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/37665 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/37665 |
| Access Level: | acceso abierto |
| Palabra clave: | F-subnormal subgroup Formation Pronormal subgroup Subnormal subgroup T-group MATEMATICA APLICADA |
| Sumario: | Let F be a formation (of finite groups) containing all nilpotent groups such that any normal subgroup of any T-group in F and any subgroup of any soluble T-group in F belongs to F. A subgroup M of a finite group G is said to be F-normal in G if G/CoreG(M) belongs to F. Named after Kegel, a subgroup U of a finite group G is called a K- F-subnormal subgroup of G if either U=G or U=U0?U1???Un=G such that Ui?1 is either normal in Ui or Ui1 is F-normal in Ui, for i=1,2,...,n. We call a finite group G a TF-group if every K- F-subnormal subgroup of G is normal in G. When F is the class of all finite nilpotent groups, the TF-groups are precisely the T-groups. The aim of this paper is to analyse the structure of the TF-groups and show that in many cases TF is much more restrictive than T. © 2011 Elsevier Inc. |
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