On products of groups and indices not divisible by a given prime

[EN] Let the group G = AB be the product of subgroupsAandB, and letpbe a prime. We prove thatpdoes not divide the conjugacy class size (index) of eachp-regular element of prime power order x is an element of A boolean OR B if and only if G is p-decomposable, i.e. G = Op(G) x Op '(G)

Detalles Bibliográficos
Autores: Felipe Román, María Josefa|||0000-0002-6699-3135, Martínez-Pastor, Ana|||0000-0002-0208-4098, Sotomayor, Víctor|||0000-0001-8649-5742, Kazarin, Lev S.
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:10251/176990
Acceso en línea:https://riunet.upv.es/handle/10251/176990
Access Level:acceso abierto
Palabra clave:Finite groups
Products of groups
Conjugacy classes
P-structure
Prime graph
Almost simple groups
MATEMATICA APLICADA
Descripción
Sumario:[EN] Let the group G = AB be the product of subgroupsAandB, and letpbe a prime. We prove thatpdoes not divide the conjugacy class size (index) of eachp-regular element of prime power order x is an element of A boolean OR B if and only if G is p-decomposable, i.e. G = Op(G) x Op '(G)