On closed subgroups of precompact groups
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadatos
Título
On closed subgroups of precompact groupsFecha de publicación
2022-09-28Editor
De GruyterISSN
1433-5883; 1435-4446Cita bibliográfica
Hernández, S., Remus, D. & Trigos-Arrieta, F. (2023). On closed subgroups of precompact groups. Journal of Group Theory, 26(3), 571-610. https://doi.org/10.1515/jgth-2022-0093Tipo de documento
info:eu-repo/semantics/articleVersión
info:eu-repo/semantics/acceptedVersionPalabras clave / Materias
Resumen
It is a Theorem of W. W. Comfort and K. A. Ross that if G is a subgroup
of a compact Abelian group, and S denotes those continuous homomorphisms from G
to the one-dimensional torus, then the topology on G is the ... [+]
It is a Theorem of W. W. Comfort and K. A. Ross that if G is a subgroup
of a compact Abelian group, and S denotes those continuous homomorphisms from G
to the one-dimensional torus, then the topology on G is the initial topology given by
S. Assume that H is a subgroup of G. We study how the choice of S affects the
topological placement and properties of H in G. Among other results, we have made
signi cant progress toward the solution of the following speci c questions: How many
totally bounded group topologies does G admit such that H is a closed (dense) subgroup?
If CS denotes the poset of all subgroups of G that are S-closed, ordered by inclusion, does
CS have a greatest (resp. smallest) element? We say that a totally bounded (topological,
resp.) group is an SC-group (topologically simple, resp.) if all its subgroups are closed
(if G and feg are its only possible closed normal subgroups, resp.) In addition, we
investigate the following questions. How many SC-(topologically simple totally bounded,
resp.) group topologies does an arbitrary Abelian group G admit? [-]
Publicado en
Journal of Group TheoryEntidad financiadora
Ministerio de Economía y Competitividad | Universitat Jaume I
Código del proyecto o subvención
MTM/PID2019-106529GB-I00 | UJI-B2019-06
Derechos de acceso
© 2022 Walter de Gruyter GmbH, Berlin/Boston
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info:eu-repo/semantics/openAccess
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info:eu-repo/semantics/openAccess
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