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4. Semisymmetric elementary abelian covers of the Möbius-Kantor graphAleksander Malnič, Dragan Marušič, Štefko Miklavič, Primož Potočnik, 2007, original scientific article Abstract: Let ▫$\wp_N : \tilde{X} \to X$▫ be a regular covering projection of connected graphs with the group of covering transformations isomorphic to ▫$N$▫. If ▫$N$▫ is an elementary abelian ▫$p$▫-group, then the projection ▫$\wp_N$▫ is called ▫$p$▫-elementary abelian. The projection ▫$\wp_N$▫ is vertex-transitive (edge-transitive) if some vertex-transitive (edge-transitive) subgroup of Aut ▫$X$▫ lifts along ▫$\wp_N$▫, and semisymmetric if it is edge- but not vertex-transitive. The projection ▫$\wp_N$▫ is minimal semisymmetric if ▫$\wp_N$▫ cannot be written as a composition ▫$\wp_N = \wp \circ \wp_M$▫ of two (nontrivial) regular covering projections, where ▫$\pw_M$▫ is semisymmetric. Finding elementary abelian covering projections can be grasped combinatorially via a linear representation of automorphisms acting on the first homology group of the graph. The method essentially reduces to finding invariant subspaces of matrix groups over prime fields (see [A. Malnic, D. Marušic, P. Potocnik, Elementary abelian covers of graphs, J. Algebraic Combin. 20 (2004) 71-97]). In this paper, all pairwise nonisomorphic minimal semisymmetric elementary abelian regular covering projections of the Möbius-Kantor graph, the Generalized Petersen graph GP(8,3), are constructed. No such covers exist for ▫$p=2$▫. Otherwise, the number of such covering projections is equal to ▫$(p-1)/4$▫ and ▫$1+(p-1)/4$▫ in cases ▫$p \equiv 5,9,13,17,21 \pmod{24}$▫ and ▫$p \equiv 1 \pmod{24}$▫, respectively, and to ▫$(p+1)/4$▫ and ▫$1+(p+1)/4$▫ in cases ▫$p \equiv 3,7,11,15,23 \pmod{24}$▫ and ▫$p \equiv 19 \pmod{24}$▫, respectively. For each such covering projection the voltage rules generating the corresponding covers are displayed explicitly. Keywords: mathematics, graph theory, graph, covering projection, lifting automorphisms, homology group, group representation, matrix group, invariant subspaces Published in RUP: 02.04.2017; Views: 2774; Downloads: 90 Link to full text |
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6. More language(s) - more space(s)? : reflections on the representation of heteroglossia and minority languages in the Alpe-Adria regionNada Zerzer, 2009, original scientific article Abstract: This article addresses the issue how heteroglossic people in the three regions of Carinthia, Primorska, and the Trst/Trieste region experience their multilingualism and its representations in everyday day life. The approach is transdisciplinary and includes theory and methods from fields of political theory, sociology of space, sociolinguistics, ethnography, visual cultures and multimodal discourse analysis. The research focus is on social constructions of space, created by heteroglossic people in their everyday life and by the representations of the languages in their living environment. This article wants to take a closer look at life with - or in - heteroglossia and at possible integrative handling of it Keywords: heteroglossia, public space, representation, language minorities, ethnic minorities, visual culture, geosemiotics, Alpe-Adria region Published in RUP: 10.07.2015; Views: 4344; Downloads: 35 Link to full text |