Supersolvability Of Product Arrangement And A Program

The thesis consists of two parts. The first part is divided into four chapters and is mainly about basic elements of hyperplanes. The second part is chapter 5, a program, for determining whether the given arrangement is supersolvable, is given by using C language.In chapter 1, the basic notion about arrangements is introduced briefly, and a lemma is given, which establish relations between the rank of matrixs and the rank of arrangements. In chapter 2, several operation characters in the lattice of product arrangement have been educed. In chapter 3 and chapter 4, it is proven that a product arrangement is supersolvable if, and only if, each factor arrangement is also supersolvable . It is also proven that if each factor arrangement has a nice partition, then the product arrangement has also a nice partition.In chapter 5, a program, for determining whether the given arrangement is supersolvable, is given by using C language, including the necessary notes and analyses. In the end, some applications of the program are given. For supersolvable arrangement, a maximal chain of modular elements is computed in the program.