Finite Groups

Finite groups are among the most fascinating mathematical objects. In particular, this field of study is interesting because

• it involves aspects of linear algebra, number theory and geometry,
• due to the finiteness of the groups very strong and interesting statements are possible,
• groups can describe symmetries, and symmetries are beautiful and
• finite groups have a huge range of applications.

For a summary of the basic definitions and theorems of the theory of finite groups see appendix A of my diploma thesis. More advanced topics are covered in the review article Finite flavour groups of fermions. My research work mainly concentrated on the finite subgroups of U(3) and SU(3). For a talk on the finite subgroups of SU(3), see the section talks. There you can also find a talk on helpful tools in finite group theory.

The image below shows the classification of the finite subgroups of SU(3).