Počet záznamov: 1
Decomposition of skew-morphisms of cyclic groups
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$a eng 102 $a SI 200 1-
$a Decomposition of skew-morphisms of cyclic groups $f István Kovács, Roman Nedela 330 $a 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 [...] 463 -1
$1 001 umb_un_cat*0297012 $1 011 $a 1855-3966 $1 011 $a 1855-3974 $1 200 1 $a Ars Mathematica Contemporanea $v Vol. 4, no. 2 (2011), pp. 329-349 $1 210 $a Koper $c Univerza na Primorskem $d 2011 606 0-
$3 umb_un_auth*0197794 $a skew-morphisms 606 0-
$3 umb_un_auth*0142750 $a product of cyclic groups 606 0-
$3 umb_un_auth*0035648 $a decomposition 615 $n 51 $a Matematika $2 konspekt 675 $a 51 $v 3. $z slo 700 -1
$3 umb_un_auth*0197795 $a Kovács $b István $4 070 $9 50 701 -0
$3 umb_un_auth*0001645 $a Nedela $b Roman $f 1960- $p UMBFP10 $9 50 $4 070 $T Katedra matematiky 801 -0
$a SK $b BB301 $g AACR2 $9 unimarc sk T85 $x existuji fulltexy
Počet záznamov: 1