On the NBC-bases of product hypersolvable arrangements

Abstract EN

This paper aims centered around the product of hypersolvable arrangements by using the hypersolvable partition analogue by proving that each of A and B are hypersolvable if A × B is a hypersolvable, also each of A and B are supersolvable if A × B is supersolvable.

Moreover, this paper show how to prove that the dimension of the first non-vanishing higher homotopy groups of the complement M(A × B) is p(A × B)× min{p(A), p(B)}.