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Decomposition of skew-morphisms of cyclic groups
Názov Decomposition of skew-morphisms of cyclic groups Aut.údaje István Kovács, Roman Nedela Autor Kovács István (50%)
Spoluautori Nedela Roman 1960- (50%) UMBFP10 - Katedra matematiky
Zdroj.dok. Ars Mathematica Contemporanea. Vol. 4, no. 2 (2011), pp. 329-349. - Koper : Univerza na Primorskem, 2011 Kľúč.slová skew-morphisms product of cyclic groups decomposition Jazyk dok. angličtina Krajina Slovinsko Systematika 51 Anotácia 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 [...] Kategória publikačnej činnosti ADC Číslo archívnej kópie 20294 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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