On the solvability of groups with four class sizes

It is shown that if the set of conjugacy class sizes of a finite group G is {1,m,n,mn}, where m, n are positive integers which do not divide each other, then G is up to central factors a {p,q}-group. In particular, G is solvable.

Detalles Bibliográficos
Autores: Beltrán, Antonio, Felipe Román, María Josefa|||0000-0002-6699-3135
Tipo de recurso: artículo
Fecha de publicación:2012
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:10251/60338
Acceso en línea:https://riunet.upv.es/handle/10251/60338
Access Level:acceso abierto
Palabra clave:Finite groups
Conjugacy class sizes
Solvable groups
MATEMATICA APLICADA
Descripción
Sumario:It is shown that if the set of conjugacy class sizes of a finite group G is {1,m,n,mn}, where m, n are positive integers which do not divide each other, then G is up to central factors a {p,q}-group. In particular, G is solvable.