Groups with normality conditions for subgroups of infinite rank
A well-known theorem of B. H. Neumann states that a group has finite conjugacy classes of subgroups if and only if it is central-by-finite. It is proved here that if G is a generalized radical group of infinite rank in which the conjugacy classes of subgroups of infinite rank are finite, then every...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:119030 |
| Acceso en línea: | https://ddd.uab.cat/record/119030 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_58214_16 |
| Access Level: | acceso abierto |
| Palabra clave: | Almost normal subgroup Group of infinite rank |
| Sumario: | A well-known theorem of B. H. Neumann states that a group has finite conjugacy classes of subgroups if and only if it is central-by-finite. It is proved here that if G is a generalized radical group of infinite rank in which the conjugacy classes of subgroups of infinite rank are finite, then every subgroup of G has finitely many conjugates, and so G=Z(G) is finite. Corresponding results are proved for groups in which every subgroup of infinite rank has fiznite index in its normal closure, and for those in which every subgroup of infinite rank is finite over its core. |
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