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...

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Detalles Bibliográficos
Autores: Beltrán, Antonio, Felipe Román, María Josefa|||0000-0002-6699-3135
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
Descripción
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.