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 .