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Homomorphic encoders of profinite abelian groups I
dc.contributor.author | Ferrer, María V. | |
dc.contributor.author | Hernández, Salvador | |
dc.date.accessioned | 2023-02-06T10:30:31Z | |
dc.date.available | 2023-02-06T10:30:31Z | |
dc.date.issued | 2023-05 | |
dc.identifier.citation | 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. | ca_CA |
dc.identifier.uri | http://hdl.handle.net/10234/201538 | |
dc.description.abstract | 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 | ca_CA |
dc.description.sponsorShip | Funding for open access charge: CRUE-Universitat Jaume I | |
dc.format.extent | 17 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Elsevier | ca_CA |
dc.relation.isPartOf | Journal of Pure and Applied Algebra, Volume 227, Issue 5, May 2023, 107305 | ca_CA |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | ca_CA |
dc.subject | Profinite abelian group | ca_CA |
dc.subject | Weakly controllable group | ca_CA |
dc.subject | Order controllable group | ca_CA |
dc.subject | Group code | ca_CA |
dc.subject | Generating set | ca_CA |
dc.subject | Homomorphic encoder | ca_CA |
dc.title | Homomorphic encoders of profinite abelian groups I | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1016/j.jpaa.2022.107305 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion | ca_CA |
project.funder.name | Ministerio de Economía y Competitividad | ca_CA |
project.funder.name | Universitat Jaume I | ca_CA |
oaire.awardNumber | MTM/PID2019-106529GB-I00 | ca_CA |
oaire.awardNumber | UJI-B2022-39 | ca_CA |
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