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  1. TitleDecomposition of skew-morphisms of cyclic groups
    Author infoIstván 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  
    LanguageEnglish
    CountrySlovenia
    systematics 51
    AnnotationA 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 Copy20294
    Catal.org.BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici
    Databasexpca - PUBLIKAČNÁ ČINNOSŤ
    ReferencesPERIODIKÁ-Súborný záznam periodika
  2. TitleVertex transitive maps on the Klein bottle
    Par.titleVrcholovo-tranzitívne mapy na Kleinovej fľaši
    Author infoOndrej Šuch
    Author Šuch Ondrej 1972- (100%) UMBFP05 - Katedra informatiky
    Source document Ars Mathematica Contemporanea. Vol. 4, no. 2 (2011), pp. 363-374. - Koper : Univerza na Primorskem, 2011
    NoteBibl.: s. 373-374
    Keywords Klein bottle   Wallpaper group   vrcholovo-tranzitívne mapy - Vertex-transitive maps   Kleinova fľaša   tapetová grupa  
    LanguageEnglish
    CountrySlovak Republic
    systematics 004
    AnnotationRes. angl.
    Public work category ADE
    No. of Archival Copy20749
    Catal.org.BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici
    Databasexpca - PUBLIKAČNÁ ČINNOSŤ
    ReferencesPERIODIKÁ-Súborný záznam periodika
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