Solvability of normal subgroups and G-class sizes
[EN] We study the solvability of a normal subgroup N of a finite group G having exactly three G-conjugacy class sizes. We show that if the set of G-class sizes of N is {1, m, mpa }, with p a prime not dividing m, then N is solvable. Thus, we get a partial extension for normal subgroups on N. Itˆo’s...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| 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:10251/68264 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/68264 |
| Access Level: | acceso abierto |
| Palabra clave: | Finite groups Conjugacy class sizes Solvable groups MATEMATICA APLICADA |
| Sumario: | [EN] We study the solvability of a normal subgroup N of a finite group G having exactly three G-conjugacy class sizes. We show that if the set of G-class sizes of N is {1, m, mpa }, with p a prime not dividing m, then N is solvable. Thus, we get a partial extension for normal subgroups on N. Itˆo’s theorem on the solvability of groups having exactly three class sizes. |
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