Full metadata record
| DC pole | Hodnota | Jazyk |
|---|---|---|
| dc.contributor.author | Feng, Yan-Quan | |
| dc.contributor.author | Hu, Kan | |
| dc.contributor.author | Nedela, Roman | |
| dc.contributor.author | Škoviera, Martin | |
| dc.contributor.author | Wang, Na-Er | |
| dc.date.accessioned | 2021-01-11T11:00:22Z | - |
| dc.date.available | 2021-01-11T11:00:22Z | - |
| dc.date.issued | 2020 | |
| dc.identifier.citation | FENG, Y., HU, K., NEDELA, R., ŠKOVIERA, M., WANG, N. Complete regular dessins and skew-morphisms of cyclic groups. Ars mathematica contemporanea, 2020, roč. 18, č. 2, s. 289-307. ISSN 1855-3966. | cs |
| dc.identifier.issn | 1855-3966 | |
| dc.identifier.uri | 2-s2.0-85095597179 | |
| dc.identifier.uri | http://hdl.handle.net/11025/42415 | |
| dc.description.abstract | Grothendickov dezén je celulární dekompozice orientovatelné kompaktní souvislé plochy s bipartitním grafem s fixovaným 2-obarvením uzlů. V článku studujeme dezény, kterých graf je kompletní bipartitní graf Km,n a grupa automorfismů je tranzitivní na množině hran. V práci dokazujeme souvis kompletních regulárních (m,n)-dezénů s dvojicemi recipročných kosomorfizmů cyklických grup řádu m a n. Práce obsahuje klasifikaci dezénů v případě, že existuje jediný dezén pro dané m a n. | cs |
| dc.format | 19 s. | cs |
| dc.format.mimetype | application/pdf | |
| dc.language.iso | en | en |
| dc.publisher | Society of Mathematicians, Physicists and Astronomers of Slovenia | en |
| dc.relation.ispartofseries | Ars Mathematica Contemporanea | en |
| dc.rights | © Society of Mathematicians, Physicists and Astronomers of Slovenia | en |
| dc.subject | Grothendieckuv dezén, grupa automorfismů, kompletní bipartitní graf, kosomorfismy grup, cyklické grupy | cs |
| dc.title | Complete regular dessins and skew-morphisms of cyclic groups | en |
| dc.title.alternative | Úplné regulární dezény a kosomorfismy cyklických grup | cs |
| dc.type | článek | cs |
| dc.type | article | en |
| dc.rights.access | openAccess | en |
| dc.type.version | publishedVersion | en |
| dc.description.abstract-translated | A dessin is a 2-cell embedding of a connected 2-coloured bipartite graph into an orientable closed surface. A dessin is regular if its group of orientation- and colour-preserving automorphisms acts regularly on the edges. In this paper we study regular dessins whose underlying graph is a complete bipartite graph Km;n, called (m; n)-complete regular dessins. The purpose is to establish a rather surprising correspondence between (m; n)- complete regular dessins and pairs of skew-morphisms of cyclic groups. A skew-morphism of a finite group A is a permutation of A that satisfies the identity f(xy) = f(x)(f(y))^p(x) for some indeger valued function defined on A , moreover, f fixes the neutral element of A. We show that every (m; n)-complete regular dessin D determines a pair of reciprocal skew-morphisms of the cyclic groups Z_n and Z_m. Conversely, D can be reconstructed from such a reciprocal pair. As a consequence, we prove that complete regular dessins, exact bicyclic groups with a distinguished pair of generators, and pairs of reciprocal skew-morphisms of cyclic groups are all in a one-to-one correspondence. Finally, we apply the main result to determining all pairs of integers m and n for which there exists, up to interchange of colours, exactly one isomorphism class of (m; n)-complete regular dessins. We show that the latter occurs precisely when every group expressible as a product of cyclic groups of order m and n is abelian, which eventually comes down to the condition gcd(m; e(n)) = gcd(e(m); n) = 1, where e is Euler’s totient function. | en |
| dc.subject.translated | Grothendieck dessin, automorphism group, complete bipartite graph, skew-morphism, cyclic group | en |
| dc.identifier.doi | 10.26493/1855-3974.1748.ebd | |
| dc.type.status | Peer-reviewed | en |
| dc.identifier.document-number | 581926200007 | |
| dc.identifier.obd | 43930630 | |
| dc.project.ID | LO1506/PUNTIS - Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnost | cs |
| Vyskytuje se v kolekcích: | Články / Articles (NTIS) Články / Articles (KMA) OBD | |
Soubory připojené k záznamu:
| Soubor | Velikost | Formát | |
|---|---|---|---|
| 1748-10258-1-PB.pdf | 326,83 kB | Adobe PDF | Zobrazit/otevřít |
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