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Title Decomposition of skew-morphisms of cyclic groups Author info István Kovács, Roman Nedela Author Kovács István (50%)
Co-authors Nedela Roman 1960- (50%) UMBFP10 - Katedra matematiky
Source document Ars Mathematica Contemporanea. Vol. 4, no. 2 (2011), pp. 329-349. - Koper : Univerza na Primorskem, 2011 Keywords skew-morphisms product of cyclic groups decomposition Language English Country Slovenia systematics 51 Annotation A skew-morphism of a group H is a permutation a of its elements fixing the identity such that for every x, y is an element of H there exists an integer k such that sigma(xy) = sigma(x)a(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 Z(n) : if n = n(1)n(2) such that (n(1), n(2)) = 1, and (n(1), phi(n(2))) = (phi(n(1)), n(2)) = 1 (phi denotes Euler's function) then all skew-morphisms sigma of Z(n) are obtained as sigma = sigma(1) x sigma(2), where sigma(i) are skew-morphisms of Z(ni) i = 1, 2. As a consequence we obtain the following result: All skew-m [...] Public work category ADC No. of Archival Copy 20294 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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Názov Vertex transitive maps on the Klein bottle Súbež.n. Vrcholovo-tranzitívne mapy na Kleinovej fľaši Aut.údaje Ondrej Šuch Autor Šuch Ondrej 1972- (100%) UMBFP05 - Katedra informatiky
Zdroj.dok. Ars Mathematica Contemporanea. Vol. 4, no. 2 (2011), pp. 363-374. - Koper : Univerza na Primorskem, 2011 Poznámka Bibl.: s. 373-374 Kľúč.slová Klein bottle Wallpaper group vrcholovo-tranzitívne mapy - Vertex-transitive maps Kleinova fľaša tapetová grupa Jazyk dok. angličtina Krajina Slovenská republika Systematika 004 Anotácia Res. angl. Kategória publikačnej činnosti ADE Číslo archívnej kópie 20749 Katal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Báza dát xpca - PUBLIKAČNÁ ČINNOSŤ Odkazy PERIODIKÁ-Súborný záznam periodika 
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