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...

Minimal, strongly proximal actions of locally compact groups on compact spaces, also known as boundary actions, were introduced by Furstenberg in the study of Lie groups. In particular, the action of a semi-simple real Lie group G on homogeneous spaces G/Q where Q ⊂ G is a parabolic subgroup, are boundary actions. Countable discrete groups admit a wide variety of boundary actions. In this note ...

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.