Given a bowtie decomposition of the complete graph Kv admitting an automorphism group G acting transitively on the vertices of the graph, we give necessary conditions involving the rank of the group and the cycle types of the permutations in G. These conditions yield non–existence results for instance when G is the dihedral group of order 2v, with v ≡ 1, 9 (mod 12), or a group acting transitive...

A subgroup of the automorphism group a graph acts half-arc-transitively on if it transitively vertex-set and edge-set but not arc-set graph. If full half-arc-transitively, is said to be half-arc-transitive. In 1994 Gardiner Praeger introduced two families tetravalent arc-transitive graphs, called C±1 C±ε that play prominent role in characterization graphs admitting an automorphisms with normal ...

Let G be the group of rational points of a connected reductive p-adic group and let K be a maximal compact subgroup satisfying conditions of Theorem 5 from Harish-Chandra (1970). Generalized spherical functions on G are eigenfunctions for the action of the Bernstein center, which satisfy a transformation property for the action of K. In this paper we show that spaces of generalized spherical fu...

We address the problem of necessary conditions and topological obstructions for existence robustly transitive endomorphisms on surfaces. Concretely, we show that a weak form hyperbolicity (namely, partial hyperbolicity) is condition in order to have displaying critical points, only surfaces supporting this class systems are either torus or Klein bottle. Furthermore, also prove induced action by...

¡v in this paper we consider a strongly regular relation ƒá on hypermodules so that the quotient is amodule (with abelian group) over a fundamental commutative ring. also, we state necessary and sufficientconditions so that the relation ƒá is transitive, and finally we prove that ƒá is transitive on hypermodules.

We study the equivalence problem of submanifolds with respect to a transitive pseudogroup action. The corresponding differential invariants are determined via formal theory and lead to the notions of l-variants and l-covariants, even in the case of non-integrable pseudogroup. Their calculation is based on the cohomological machinery: We introduce a complex for covariants, define their cohomolog...

CNRS, Université de Rennes-1 and Technische Universität Graz We study the Poisson boundary (≡ representation of bounded harmonic functions) of Markov operators on discrete state spaces that are invariant under the action of a transitive group of permutations. This automorphism group is locally compact, but not necessarily discrete or unimodular. The main technical tool is the entropy theory whi...

(g, x) → gx : G × X → X such that ex = x for every x in X and g(hx) = (gh)x for g and h in G and x in X (here e denotes the neutral element of G). It is easily seen that for each g in G the map x → gx is a homeomorphism of X whose inverse is the map x → g−1x . If x belongs to X and U is a subset of G, then U x = {gx : g ∈ U}. The action of G on X is transitive if Gx = X for every x in X . It is...