Doubly transitive groups and cyclic quandles

Autores
Vendramin, Claudio Leandro
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove that for n > 2 there exists a quandle of cyclic type of size n if and only if n is a power of a prime number. This establishes a conjecture of S. Kamada, H. Tamaru and K. Wada. As a corollary, every finite quandle of cyclic type is an Alexander quandle. We also prove that finite doubly transitive quandles are of cyclic type. This establishes a conjecture of H. Tamaru.
Fil: Vendramin, Claudio Leandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Doubly-Transitive Groups
Finite Quandles
Quandles of Cyclic Type
Two-Point Homogeneous Quandles
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/55429
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/55429
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network_name_str CONICET Digital (CONICET)
spelling Doubly transitive groups and cyclic quandlesVendramin, Claudio LeandroDoubly-Transitive GroupsFinite QuandlesQuandles of Cyclic TypeTwo-Point Homogeneous Quandleshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove that for n > 2 there exists a quandle of cyclic type of size n if and only if n is a power of a prime number. This establishes a conjecture of S. Kamada, H. Tamaru and K. Wada. As a corollary, every finite quandle of cyclic type is an Alexander quandle. We also prove that finite doubly transitive quandles are of cyclic type. This establishes a conjecture of H. Tamaru.Fil: Vendramin, Claudio Leandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaMathematical Society of Japan2017-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/55429Vendramin, Claudio Leandro; Doubly transitive groups and cyclic quandles; Mathematical Society of Japan; Journal Of The Mathematical Society Of Japan; 69; 3; 7-2017; 1051-10570025-5645CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.2969/jmsj/06931051info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.jmsj/1499846516info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:32:20Zoai:ri.conicet.gov.ar:11336/55429instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:32:20.478CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Doubly transitive groups and cyclic quandles
title Doubly transitive groups and cyclic quandles
spellingShingle Doubly transitive groups and cyclic quandles
Vendramin, Claudio Leandro
Doubly-Transitive Groups
Finite Quandles
Quandles of Cyclic Type
Two-Point Homogeneous Quandles
title_short Doubly transitive groups and cyclic quandles
title_full Doubly transitive groups and cyclic quandles
title_fullStr Doubly transitive groups and cyclic quandles
title_full_unstemmed Doubly transitive groups and cyclic quandles
title_sort Doubly transitive groups and cyclic quandles
dc.creator.none.fl_str_mv Vendramin, Claudio Leandro
author Vendramin, Claudio Leandro
author_facet Vendramin, Claudio Leandro
author_role author
dc.subject.none.fl_str_mv Doubly-Transitive Groups
Finite Quandles
Quandles of Cyclic Type
Two-Point Homogeneous Quandles
topic Doubly-Transitive Groups
Finite Quandles
Quandles of Cyclic Type
Two-Point Homogeneous Quandles
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We prove that for n > 2 there exists a quandle of cyclic type of size n if and only if n is a power of a prime number. This establishes a conjecture of S. Kamada, H. Tamaru and K. Wada. As a corollary, every finite quandle of cyclic type is an Alexander quandle. We also prove that finite doubly transitive quandles are of cyclic type. This establishes a conjecture of H. Tamaru.
Fil: Vendramin, Claudio Leandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We prove that for n > 2 there exists a quandle of cyclic type of size n if and only if n is a power of a prime number. This establishes a conjecture of S. Kamada, H. Tamaru and K. Wada. As a corollary, every finite quandle of cyclic type is an Alexander quandle. We also prove that finite doubly transitive quandles are of cyclic type. This establishes a conjecture of H. Tamaru.
publishDate 2017
dc.date.none.fl_str_mv 2017-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/55429
Vendramin, Claudio Leandro; Doubly transitive groups and cyclic quandles; Mathematical Society of Japan; Journal Of The Mathematical Society Of Japan; 69; 3; 7-2017; 1051-1057
0025-5645
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55429
identifier_str_mv Vendramin, Claudio Leandro; Doubly transitive groups and cyclic quandles; Mathematical Society of Japan; Journal Of The Mathematical Society Of Japan; 69; 3; 7-2017; 1051-1057
0025-5645
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.2969/jmsj/06931051
info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.jmsj/1499846516
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Mathematical Society of Japan
publisher.none.fl_str_mv Mathematical Society of Japan
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844612985584091136
score 13.070432

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