/manager/Index ${session.getAttribute("locale")} 5 Decompositions of locally compact contraction groups, series and extensions /manager/Repository/uon:38290 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}→Fp((t))→G→Fp((t))→{0}of the additive group of the field of formal Laurent series over Fp=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 /manager/Repository/uon:38494 Mon 11 Oct 2021 14:41:00 AEDT ]]> An algebraic approach to lifts of digraphs /manager/Repository/uon:36785 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 Γα. 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 ]]>