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${session.getAttribute("locale")}5Decompositions of locally compact contraction groups, series and extensions
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n(x) →e pointwise as n →∞. We show that every surjective, continuous, equivariant homomorphism between locally compact contraction groups admits an equivariant continuous global section. As a consequence, extensions of locally compact contraction groups with abelian kernel can be described by continuous equivariant cohomology. For each prime number p, we use 2-cocycles to construct uncountably many pairwise non-isomorphic totally disconnected, locally compact contraction groups (G, α)which are central extensions{0}→F_{p}((t))→G→F_{p}((t))→{0}of the additive group of the field of formal Laurent series over F_{p}=Z/pZby itself. By contrast, there are only countably many locally compact contraction groups (up to isomorphism) which are torsion groups and abelian, as follows from a classification of the abelian locally compact contraction groups.]]>Thu 26 Aug 2021 14:13:11 AEST]]>An improved Moore bound and some new optimal families of mixed Abelian Cayley graphs
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Mon 11 Oct 2021 14:41:00 AEDT]]>An algebraic approach to lifts of digraphs
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α of a voltage digraph, which has arcs weighted by the elements of a group. As a main result, when the involved group is Abelian, we completely determine the spectrum of Γ^{α}. As some examples of our technique, we study some basic properties of the Alegre digraph, and completely characterize the spectrum of a new family of digraphs, which contains the generalized Petersen graphs, and the Hoffman-Singleton graph.]]>Mon 06 Jul 2020 09:53:43 AEST]]>