Representation of group isomorphisms I
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Otros documentos de la autoría: Ferrer González, María Vicenta; Gary Gutierrez, Margarita; Hernández, Salvador
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INVESTIGACIONMetadatos
Título
Representation of group isomorphisms IFecha de publicación
2019-08-15Editor
ElsevierISSN
0166-8641; 1879-3207Cita bibliográfica
Ferrer, M. V.; Gary, M.; Hernández, S. "Representation of Group Isomorphisms I." Topology and its Applications, 2019, vol. 263, p. 44-60Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.sciencedirect.com/science/article/pii/S0166864119301592Versión
info:eu-repo/semantics/acceptedVersionResumen
Let G be a metric group and let Aut(G) denote the automorphism group
of G. If A and B are groups of G-valued maps defined on the sets X and Y , respec-
tively, we say that A and B are equivalent if there is a group ... [+]
Let G be a metric group and let Aut(G) denote the automorphism group
of G. If A and B are groups of G-valued maps defined on the sets X and Y , respec-
tively, we say that A and B are equivalent if there is a group isomorphism H: A ! B
such that there is a bijective map h: Y ! X and a map w: Y ! Aut(G) satisfy-
ing Hf(y) = w[y](f(h(y))) for all y 2 Y and f 2 A. In this case, we say that H
is represented as a weighted composition operator. A group isomorphism H defined
between A and B is called separating when for each pair of maps f; g 2 A satisfying
that f-1(eG)[g-1(eG) = X, it holds that (Hf)-1(eG)[(Hg)-1(eG) = Y . Our main
result establishes that under some mild conditions, every separating group isomor-
phism can be represented as a weighted composition operator. As a consequence we
establish the equivalence of two function groups if there is a biseparating isomorphism
defined between them. [-]
Publicado en
Topology and its Applications, 2019, vol. 263, p. 44-60Proyecto de investigación
Research Partially supported by the Spanish Ministerio de Economía y Competitividad, grant MTM2016-77143-P (AEI/FEDER, EU), and the Universitat Jaume I, grant P1171B2015-77.Derechos de acceso
info:eu-repo/semantics/openAccess
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