The transitivity degree of a group $G$ is the supremum all integers $k$ such that admits faithful $k$-transitive action. Few obstructions are known to impose an upper bound on for infinite groups. results this article provide two new classes groups whose can be computed, as corollary classification $3$-transitive actions these More precisely, suppose subgroup homeomorphism circle $\mathsf{Homeo...

This paper is devoted to the classification of flag-transitive 2-(v,k,2) designs. We show that apart from two known symmetric 2-(16,6,2) designs, every subgroup G automorphism group a nontrivial design primitive affine or almost simple type. Moreover, we classify designs admitting flag transitive with socle PSL(n,q) for some n≥3. Alongside this analysis give construction 2-(v,k−1,k−2) given 2-(...

The action of a subgroup G of automorphisms of a graph X is said to be 2 -transitive if it is vertexand edgebut not arc-transitive. In this case the graph X is said to be (G, 2)-transitive. In particular, X is 1 2 -transitive if it is (Aut X, 1 2)-transitive. The 2 -transitive action of G on X induces an orientation of the edges of X which is preserved by G. Let X have valency 4. An even length...

Ge asked the question whether $LF_{\infty}$ can be embedded into $LF_2$ as a maximal subfactor. We answer it affirmatively by three different approaches, all containing same key ingredient: existence of subgroups with infinite index. also show that point stabilizer for every faithful, 4-transitive action on an set give rise to von Neumann subalgebras. Combining this known results constructing h...

We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space En = G/K where G is the semidirect product Rn · K of the translation group with a closed subgroup K of the orthogonal group O(n). We give exact parameterizations of the space of (G,K)–spherical functions by a certain affine algebraic variety, and of the positive definite on...

Several results on the action of graph automorphisms on ends and fibers are generalized for the case of metric ends. This includes results on the action of the automorphisms on the end space, directions of automorphisms, double rays which are invariant under a power of an automorphism and metrically almost transitive automorphism groups. It is proved that the bounded automorphisms of a metrical...

It is known that there are precisely three transitive permutation groups of degree 6 admit an invariant partition with parts size 2 such the kernel action on has order 4; these called A 4 ( ) , S d and c . For each L ∈ { } we construct infinite family finite connected 6-valent graphs Γ n N arc-transitive G ≤ Aut group induced by vertex-stabiliser v neighbourhood a vertex isomorphic to L, ∣ expo...

‎darafsheh and assari in [normal edge-transitive cayley graphs on non-abelian groups of order 4p‎, ‎where $p$ is a prime number‎, ‎sci‎. ‎china math‎., ‎56 (1) (2013) 213-219.] classified the connected normal edge transitive and‎ ‎$frac{1}{2}-$arc-transitive cayley graph of groups of order $4p$‎. ‎in this paper we continue this work by classifying the‎ ‎connected cayley graph of groups of order...