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1.
Decomposition of skew-morphisms of cyclic groups
István Kovács, Roman Nedela, 2011, izvirni znanstveni članek

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 ▫$(n, \varphi(n)) = 1$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: ...A skew-morphism of a group ▫$H$▫ is a permutation ▫$\sigma$▫ of its...
Ključne besede: cyclic group, permutation group, skew-morphism, Schur ring
Objavljeno: 15.10.2013; Ogledov: 1880; Prenosov: 51
URL Polno besedilo (0,00 KB)

2.
A note on finite non-solvable groups with few non-cyclic subgroups
Jiangtao Shi, Cui Zhang, 2011, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...finite group, non-cyclic subgroup, non-solvable group, ...
Ključne besede: finite group, non-cyclic subgroup, non-solvable group
Objavljeno: 15.10.2013; Ogledov: 1152; Prenosov: 18
URL Polno besedilo (0,00 KB)

3.
Cyclic groups are CI-groups for balanced configurations
Mikhail Muzychuk, Dragan Marušič, István Kovács, Sergio Hiroki Koike Quintanar, 2018, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...Cayley object, CI-property, cyclic group, balanced configuration...
Ključne besede: Cayley object, CI-property, cyclic group, balanced configuration
Objavljeno: 20.07.2018; Ogledov: 890; Prenosov: 151
URL Polno besedilo (0,00 KB)
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