For a permutation group G acting on set V, subset I of is said to be an intersecting if for every pair elements g,h∈I there exists v∈V such that g(v)=h(v). The intersection density ρ(G) transitive the maximum value quotient |I|/|Gv| where Gv stabilizer point and runs over all sets in G. If largest then have Erdős–Ko–Rado (EKR)-property, moreover, has strict-EKR-property size coset stabilizer. I...

In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product o...

in this paper‎, ‎we determine the simple groups $g=ab$‎, ‎where $b$ is isomorphic to $l_{3}(4)$ and $a$ isomorphic to an alternating or a symmetric group on $ngeq5$‎, ‎letters‎.