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Let $D=(V(D), A(D))$ be a digraph and $k \ge 2$ an integer. We say that $D$ is $k$-quasi-transitive if for every directed path $(v_0, v_1,..., v_k)$ in $D$, then $(v_0, v_k) \in A(D)$ or $(v_k, v_0) \...
We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such...
Abstract: Formal and distributional semantic models offer complementary benefits in modeling meaning. The categorical compositional distributional (DisCoCat) model of meaning of Coecke et al. (arXiv:1...
Abstract: This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary diffe...
Abstract: For $(M,[g])$ a conformal manifold of signature $(p,q)$ and dimension at least three, the conformal holonomy group $\mathrm{Hol}(M,[g]) \subset O(p+1,q+1)$ is an invariant induced by the can...
Abstract: n [D. de Caen, E.R. van Dam. Fissioned triangular schemes via the cross-ratio, {Europ. J. Combin.}, 22 (2001) 297-301], de Caen and van Dam constructed a fission scheme $\FT(q+1)$ of the tri...
Motivated by some questions in Euclidean Ramsey theory, our aim in this note is to show that there exists a cyclic quadrilateral that does not embed into any transitive set (in any dimension). We show...
A finite set X in some Euclidean space Rn is called Ramsey if for any k there is a d such that whenever Rd is k-coloured it contains a monochromatic set congruent to X. This notion was introduced by E...
A group G acts infinitely transitively on a set Y if for every positive integer m, its action is m-transitive on Y . Given a real affine algebraic variety Y of dimension greater than or equal to 2, ...
We prove that the base size of a transitive group $G$ with solvable point stabilizer is not greater than $k$ provided the same statement holds for every group of $G$-induced automorphisms of each nona...
We give a complete characterization of abelian subgroups of GL(n, R) with a locally dense (resp. dense) orbit in R^n. For finitely generated subgroups, this characterization is explicit and it is used...
Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p~k (k ≥ 1), and let A be the full automorphism group of X. In this paper, we prove that the stabilizer Av of a vertex ...
This is a survey article on barely transitive groups. It also involves some recent results in the case of a non-locally finite barely transitive group.
We give a group theoretic proof of the splitting of sharply 2-transitive groups of characteristic 3.
B. Hartley asked the following question: Does there exist a torsion free barely transitive group? Existence of torsion free simple barely transitive group is also unknown. We answer the latter questio...

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