Abstract
According to the powerful geometric properties of the hypersolvable order on the hyperplanes of a supersolvable arrangement, we introduced a sufficient condition on the Orlik-Solomon algebra for any central arrangement to have supersolvable analogue and we showed this condition as a necessary condition (not sufficient) on the Orlik-Solomon algebra for any central arrangement to be K(π; 1). Finally as an illustration of our result, we produce to the Orlik-Solomon algebra for the complexification of the Coxeter arrangement of type Ar and Br, for r ≥ 3, a structure by their supersolvable partitions analogues.
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