A subgroup of the automorphism group a graph Γ is said to be half-arc-transitive on if its action transitive vertex set and edge but not arc Γ. Tetravalent graphs girths 3 4 admitting automorphisms have previously been characterized. In this paper we study examples girth 5. We show that, with two exceptions, all such only directed 5-cycles respect corresponding induced orientation edges. Moreov...

We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such an action, which applies for example to surface groups and fundamental groups of surface bundles over S.

The main purpose of this paper is to make an analysis of the transitive construction in speech verbs. Our starting point is Faber and Mairal’s (1999) classification of sixty-two verbs of speech. In our view, the semantic grounding of speech verbs is what determines the construction to which they are ascribed and the syntactic structure by means of which they are realised. We have approached thi...

We give examples of countable linear groups $\Gamma < \operatorname {SL}_{{\mathbf {3}}}({\mathbf {R}})$, with no nontrivial normal abelian subgroups, that admit a faithful sharply $2$-transitive action on set. Without the linearity assumption, such were recently constructed by Rips, Segev, and Tent in [J. Eur. Math. Soc. 19 (2017), pp. 2895â??2910]. Our are permutational characteristic $2$, se...

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

This note is part of a general programme to classify the automorphism groups of nite linear spaces. There have been a number of contributions to this programme including two recent surveys, 8, 3]. One of the most signiicant contributions was the classiication of ag-transitive linear spaces, 1]. Since then the eeort has been to classify the line-transitive examples. These fall naturally into two...

A code C in the Hamming metric, that is, is a subset of vertex set VΓ graph Γ=H(m,q), gives rise to natural distance partition {C,C1,…,Cρ}, where ρ covering radius C. Such called completely transitive if automorphism group Aut(C) acts transitively on each sets C, C1, …, Cρ. 2-neighbour-transitive ρ⩾2 and C1 C2. Let be binary (q=2) having full minimum δ⩾5. Then it known induces 2-homogeneous act...

The concept of spherical t-design, which is a finite subset of the unit sphere, was introduced by Delsarte-Goethals-Seidel (1977). The concept of Euclidean tdesign, which is a two step generalization of spherical design in the sense that it is a finite weighted subset of Euclidean space, by Neumaier-Seidel (1988). We first review these two concepts, as well as the concept of tight t-design, i.e...

Young children learn about causal structure not only from observation, but also from the language they hear. Two novelverb studies show that preschoolers expect transitive sentences like ‘Sarah broke the lamp’ to express relationships between cause and effect. Previous work has conflated causation with other semantic features, presenting children with coarse contrasts between scenes varying on ...

Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.