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  • Elementary abelian covers of graphs
    Malnič, Aleksander ; Marušič, Dragan ; Potočnik, Primož, 1971-
    Let ▫$\cal{C}_G(X)$▫ be the set of all (equivalence classes of) regular covers of a given connected graph ▫$X$▫ along which a given group ▫$G \le {\rm Aut}X$▫ of automorphisms lifts. There is a ... natural lattice structure on ▫$\cal{C}_G(X)$▫, where ▫$\wp_1 \le \wp_2$▫ whenever ▫$\wp_2$▫ factors through ▫$\wp_1$▫. The sublattice ▫$\cal{C}_G(\wp)$▫ of covers which are below a given cover ▫$\wp: \tilde{X} \to X$▫ naturally corresponds to lattice ▫$\cal{N}_G(\wp)$▫ of certain subgroups of the group of covering transformations. In order to study this correspondence, some general theorems regarding morphisms and decomposition of regular covering projections are proved. All theorems are stated and proved combinatorially in terms of voltage assignments in order to facilitate computation in concrete applications. Fora given prime ▫$p$▫, let ▫$\cal{C}_G^p(X) \le \cal{C}_G(X)$▫ denote the sublattice of all regular covers with an elementary abelian ▫$p$▫-group of covering transformations. There is an algorithm which explicitly constructs ▫$\cal{C}_G^p(X)$▫ in the sense that, for each member of ▫$\cal{C}_G^p(X)$▫, a concrete voltage assignment on ▫$X$▫ which determines this cover up to equivalence, is generated. The algorithm uses the well known algebraic tools for finding invariant subspaces of a given linear representation of a group. To illustrate the method an example is included.
    Vrsta gradiva - knjiga ; neleposlovje za odrasle
    Založništvo in izdelava - Ljubljana : Institute of Mathematics, Physics and Mechanics, Department of Mathematics, 2001
    Jezik - angleški
    COBISS.SI-ID - 34832387

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