Chapters authored
Group Theory from a Mathematical Viewpoint
In this chapter, for the reader who does not major in mathematics but chemistry, we discuss general group theory from a mathematical viewpoint without proofs. The main purpose of the chapter is to reduce reader’s difficulties for the abstract group theory and to get used to dealing with it. In order to do this, we exposit definitions and theorems of the field without rigorous and difficult arguments on the one hand and give lots of basic and fundamental examples for easy to understand on the other hand. Our final goal is to obtain well understandings about conjugacy classes, irreducible representations, and characters of groups with easy examples of finite groups. In particular, we give several character tables of finite groups of small order, including cyclic groups, dihedral groups, symmetric groups, and their direct product groups. In Section 8, we deal with directed graphs and their automorphism groups. It seems that some of ideas and techniques in this section are useful to consider the symmetries of molecules in chemistry.
Part of the book: Symmetry (Group Theory) and Mathematical Treatment in Chemistry