On the NBC-Bases of product hypersolvable arrangements

Abstract

         This paper aims centered around the product of hypersolvable arrangements by using the hypersolvable partition analogue by proving that each of  and  are hypersolvable if  is a hypersolvable, also each of  and  are supersolvable if  is supersolvable. Moreover, this paper show how to prove that the dimension of the first non-vanishing higher homotopy groups of the complement  is .