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Naslov:Decomposition of skew-morphisms of cyclic groups
Avtorji:Nedela, Roman (Avtor)
Kovács, István (Avtor)
Datoteke:URL http://amc.imfm.si/index.php/amc/article/view/157/139
 
Jezik:Angleški jezik
Vrsta gradiva:Delo ni kategorizirano
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:IAM - Inštitut Andrej Marušič
Opis:A skew-morphism of a group ▫$H$▫ is a permutation ▫$\sigma$▫ of its elements fixing the identity such that for every ▫$x, y \in H$▫ there exists an integer ▫$k$▫ such that ▫$\sigma (xy) = \sigma (x)\sigma k(y)$▫. It follows that group automorphisms are particular skew-morphisms. Skew-morphisms appear naturally in investigations of maps on surfaces with high degree of symmetry, namely, they are closely related to regular Cayley maps and to regular embeddings of the complete bipartite graphs. The aim of this paper is to investigate skew-morphisms of cyclic groups in the context of the associated Schur rings. We prove the following decomposition theorem about skew-morphisms of cyclic groups ▫$\mathbb Z_n$▫: if ▫$n = n_{1}n_{2}$▫ such that ▫$(n_{1}n_{2}) = 1$▫, and ▫$(n_{1}, \varphi (n_{2})) = (\varphi (n_{1}), n_{2}) = 1$▫ (▫$\varphi$▫ denotes Euler's function) then all skew-morphisms ▫$\sigma$▫ of ▫$\mathbb Z_n$▫ are obtained as ▫$\sigma = \sigma_1 \times \sigma_2$▫, where ▫$\sigma_i$▫ are skew-morphisms of ▫$\mathbb Z_{n_i}, \; i = 1, 2$▫. As a consequence we obtain the following result: All skew-morphisms of ▫$\mathbb Z_n$▫ are automorphisms of ▫$\mathbb Z_n$▫ if and only if ▫$n = 4$▫ or ▫$(n, \varphi(n)) = 1$▫.
Ključne besede:cyclic group, permutation group, skew-morphism, Schur ring
Leto izida:2011
Št. strani:str. 329-349
Številčenje:Vol. 4, no. 2
ISSN:1855-3966
UDK:519.1
COBISS_ID:1024369492 Povezava se odpre v novem oknu
Število ogledov:1631
Število prenosov:10
Metapodatki:XML RDF-CHPDL DC-XML DC-RDF
Področja:Gradivo ni uvrščeno v področja.
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Sekundarni jezik

Jezik:Angleški jezik
Ključne besede:ciklična grupa, permutacijska grupa, poševni morfizem, Schurov kolobar

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