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Indecomposable solutions of the Yang–Baxter equation of square-free cardinality

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cris.lastimport.scopus2024-02-12T19:46:48Z
dc.abstract.enIndecomposable involutive non-degenerate set-theoretic solutions of the Yang–Baxter equation of cardinality , for different prime numbers , are studied. It is proved that they are multipermutation solutions of level ≤n. In particular, there is no simple solution of a non-prime square-free cardinality. This solves a problem stated in [11] and provides a far reaching extension of several earlier results on indecomposability of solutions. The proofs are based on a detailed study of the brace structure on the permutation group associated to such a solution. It is proved that are the only primes dividing the order of . Moreover, the Sylow -subgroups of are elementary abelian -groups and if denotes the Sylow -subgroup of the additive group of the left brace , then there exists a permutation such that , are ideals of the left brace and . In addition, indecomposable solutions of cardinality that are multipermutation of level n are constructed, for every nonnegative integer n.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorOkniński, Jan
dc.contributor.authorCedó, F.
dc.date.accessioned2024-01-25T04:12:53Z
dc.date.available2024-01-25T04:12:53Z
dc.date.issued2023
dc.description.financePublikacja bezkosztowa
dc.description.volume430
dc.identifier.doi10.1016/J.AIM.2023.109221
dc.identifier.issn0001-8708
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/109170
dc.identifier.weblinkhttps://api.elsevier.com/content/article/PII:S000187082300364X?httpAccept=text/xml
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofAdvances in Mathematics
dc.relation.pages109221, 1-26
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.titleIndecomposable solutions of the Yang–Baxter equation of square-free cardinality
dc.typeJournalArticle
dspace.entity.typePublication