for two normal edge-transitive cayley graphs on groups h and k which have no common direct factor and gcd(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

Let $S_n$ be the symmetric group on the set $[n]={1, 2, ldots, n}$. For $gin S_n$ let $fix(g)$ denote the number of fixed points of $g$. A subset $S$ of $S_n$ is called $t$-emph{transitive} if for any two $t$-tuples $(x_1,x_2,ldots,x_t)$ and $(y_1,y_2,ldots ,y_t)$ of distinct elements of $[n]$, there exists $gin S$ such that $x_{i}^g=y_{i}$ for any $1leq ileq t$ and additionally $S$ is called e...

We show that if r ≥ 3 and α is a faithful Z-Cartan action on a torus T by automorphisms, then any closed subset of (T) which is invariant and topologically transitive under the diagonal Z-action by α is homogeneous, in the sense that it is either the full torus (T), or a finite set of rational points, or a finite disjoint union of parallel translates of some d-dimensional invariant subtorus. A ...

A description of transitive actions of a semisimple algebraic group G on toric varieties is obtained. Every toric variety admitting such an action lies between a product of punctured affine spaces and a product of projective spaces. The result is based on the Cox realization of a toric variety as a quotient space of an open subset of a vector space V by a quasitorus action and on investigation ...

A theory for the transitive action of a group on the configuration space of a system of fermions is shown to lead to the conclusion that bosons can be represented by the action of cosets of the group. By application of the principle to fundamental, indivisible fermions, the symplectic group Sp (n) is shown to be the largest group of isometries of the space. Interactions between particles are re...

If the permutation action ρI is transitive, all factors Xi are quasiisometric to each other, and the restricted quasi-actions Gi y Xi are quasi-conjugate (when identifying different stabilizers Gi by inner automorphisms of G). The main result of this note is that in this case any of the quasi-actions Gi y Xi determines ρ up to quasi-conjugacy, and moreover any quasi-conjugacy class may arise as...

Transitive permutation groups having a non self paired suborbit of length are investigated via the corresponding orbital graphs If G is such a group and X is the orbital graph associated with a sub orbit of length of G which is not self paired then X has valency and admits a vertex and edge but not arc transitive action of G There is a natural balanced orientation of the edge set of X induced a...

In this paper, we explore how observers of a reach-to-grasp action can identify and distinguish between the agent and patient (i.e. target) of the action. We investigate the hypothesis that there is a characteristic sequential structure to the observer's pattern of saccades, with the agent being fixated first, and then the target. We report an experiment which indicates that this sequence of sa...

The ability to reproduce visually presented actions has been studied through neuropsychological observations of patients with ideomotor apraxia. These studies include attempts to understand the neural basis of action reproduction based on lesion-symptom mapping in different patient groups. While there is a convergence of evidence that areas in the parietal and frontal lobes within the left hemi...

The determinant method of Kasteleyn gives a computing the number perfect matchings planar bipartite graph. In addition, results Bernardi exhibit bijection between spanning trees graph and elements its Jacobian. this paper, we explore an adaptation Bernardi’s results, providing simply transitive group action cokernel on set matchings, when in question is form $$G^+$$ , as defined by Kenyon, Prop...