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dc.contributor.authorFerrer González, María Vicenta
dc.contributor.authorHernández, Salvador
dc.contributor.authorShakhmatov, Dmitry
dc.date.accessioned2017-10-20T06:49:05Z
dc.date.available2017-10-20T06:49:05Z
dc.date.issued2017-09
dc.identifier.citationFERRER GONZÁLEZ, María Vicenta; HERNÁNDEZ MUÑOZ, Salvador; SHAKHMATOV, Dmitri. Subgroups of direct products closely approximated by direct sums. Forum Mathematicum (2017), v. 19, issue 5ca_CA
dc.identifier.urihttp://hdl.handle.net/10234/169464
dc.description.abstractLet I be an infinite Π set, fGi : i 2 Ig be a family of (topological) groups and G = i∈I Gi be its direct product. For J I, pJ : G ! Π j∈J Gj denotes the projection. We say that a subgroup H of G is: (i) uniformly controllable in G provided that for every finite set J I there exists a finite set K I such that pJ (H) = pJ (H \ ⊕ i∈K Gi); (ii) controllable in G provided that pJ (H) = pJ (H \⊕ i∈I Gi) for every finite set J I; (iii) weakly controllable in G if H \⊕ i∈I Gi is dense in H, when G is equipped with the Tychonoff product topology. One easily proves that (i)!(ii)!(iii). We thoroughly investigate the question as to when these two arrows can be reversed. We prove that the first arrow can be reversed when H is compact, but the second arrow cannot be reversed even when H is compact. Both arrows can be reversed if all groups Gi are finite. When Gi = A for all i 2 I, where A is an abelian group, we show that the first arrow can be reversed for all subgroups H of G if and only if A is finitely generated. Connections with coding theory are highlighted.ca_CA
dc.format.extent21 p.ca_CA
dc.format.mimetypeapplication/pdfca_CA
dc.language.isoengca_CA
dc.publisherDe Gruyterca_CA
dc.relation.isPartOfForum Mathematicum (2017), v. 29, issue 5ca_CA
dc.rights.urihttp://rightsstatements.org/vocab/CNE/1.0/*
dc.subjectControllable groupca_CA
dc.subjectWeakly controllable groupca_CA
dc.subjectFinitely generated groupca_CA
dc.subjectCompact groupca_CA
dc.subjectCoding theoryca_CA
dc.titleSubgroups of direct products closely approximated by direct sumsca_CA
dc.typeinfo:eu-repo/semantics/articleca_CA
dc.identifier.doihttps://doi.org/10.1515/forum-2016-0047
dc.relation.projectID1) Generalitat Valenciana, grant code: PROMETEO II/2014/062; 2) Universitat Jaume I, grant P11B2015-77; 3) Grant-in-Aid for Scientific Research (C) No. 22540089 by the Japan Society for the Promotion of Science (JSPS).ca_CA
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessca_CA
dc.relation.publisherVersionhttps://www.degruyter.com/view/j/form.ahead-of-print/forum-2016-0047/www.degruyter.com/view/j/form.ahead-of-print/forum-2016-0047/forum-2016-0047.xmlca_CA
dc.type.versioninfo:eu-repo/semantics/acceptedVersionca_CA


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