Homomorphic encoders of profinite abelian groups I
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Título
Homomorphic encoders of profinite abelian groups IFecha de publicación
2023-05Editor
ElsevierCita bibliográfica
FERRER, María V.; HERNÁNDEZ, Salvador. Homomorphic encoders of profinite abelian groups I. Journal of Pure and Applied Algebra, 2023, vol. 227, no 5, p. 107305.Tipo de documento
info:eu-repo/semantics/articleVersión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
Let {Gi |i ∈ N} be a family of finite Abelian groups. We say that a subgroup
G ≤
i∈N
Gi is order controllable if for every i ∈ N there is ni ∈ N such that for
each c ∈ G, there exists a ∈ G satisfying that a|[1,i] ... [+]
Let {Gi |i ∈ N} be a family of finite Abelian groups. We say that a subgroup
G ≤
i∈N
Gi is order controllable if for every i ∈ N there is ni ∈ N such that for
each c ∈ G, there exists a ∈ G satisfying that a|[1,i] = c|[1,i], supp(a) ⊆ [1, ni], and
order(a) divides order(c|[1,ni]). In this paper we investigate the structure of order
controllable subgroups. It is proved that every order controllable, profinite, abelian
group contains a subset {gn | n ∈ N} that topologically generates the group and
whose elements gn all have finite support. As a consequence, sufficient conditions
are obtained that allow us to encode, by means of a topological group isomorphism,
order controllable profinite abelian groups. Further applications of these results to
group codes will appear subsequently [-]
Publicado en
Journal of Pure and Applied Algebra, Volume 227, Issue 5, May 2023, 107305Entidad financiadora
Ministerio de Economía y Competitividad | Universitat Jaume I
Código del proyecto o subvención
MTM/PID2019-106529GB-I00 | UJI-B2022-39
Derechos de acceso
info:eu-repo/semantics/openAccess
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- IMAC_Articles [121]
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