On zeros of irreducible characters lying in a normal subgroup

[EN] Let N be a normal subgroup of a finite group G. In this paper, we consider the elements g of N such that x(g)¿0 for all irreducible characters x of G. Such an element is said to be non-vanishing in G. Let p be a prime. If all p-elements of N satisfy the previous property, then we prove that N h...

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Detalles Bibliográficos
Autores: Felipe Román, María Josefa|||0000-0002-6699-3135, Sotomayor, Víctor|||0000-0001-8649-5742, Grittini, N.
Tipo de recurso: artículo
Fecha de publicación:2020
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:10251/166202
Acceso en línea:https://riunet.upv.es/handle/10251/166202
Access Level:acceso abierto
Palabra clave:Finite groups
Normal subgroups
Irreducible characters
Conjugacy classes
MATEMATICA APLICADA
Descripción
Sumario:[EN] Let N be a normal subgroup of a finite group G. In this paper, we consider the elements g of N such that x(g)¿0 for all irreducible characters x of G. Such an element is said to be non-vanishing in G. Let p be a prime. If all p-elements of N satisfy the previous property, then we prove that N has a normal Sylow p-subgroup. As a consequence, we also study certain arithmetical properties of the G-conjugacy class sizes of the elements of N which are zeros of some irreducible character of G. In particular, if N=G, then new contributions are obtained.