CHARACTERS OF FINITE ABELIAN GROUPS

• Main Author: Rais, Fadhli
• Format: Final Project
• Language: Indonesia
• Subjects: Aljabar
• Online Access: https://digilib.itb.ac.id/gdl/view/32733
• Institution: Institut Teknologi Bandung

Algebra is a field in mathematics that is very interesting for studied. The development of research in this field is growing rapidly. Discussions in the field of abstract algebra, especially in problems relating to groups, considerate the big attention from algebra lovers to be studied is the characters in finite abelian groups. Character which is a homomorphism of the group G to S1 was not as simple which is thought, but many things can be extracted from this mapping. Character in finite abelian groups was first studied and applied in number theory, that is when Dirichlet use character from (Z=(m)) to prove when (a;m) = 1, then there are many prime pamodm that satisfy the problem. In addition, characters in finite abelian group can simplify the form of the Fourier series. In its application, it can be applied in the world of engineering such as techniques of signal processing, and error correction codes. In this final project, the characters will be closed in finite abelian group and its properties. In addition it will be discussed about the dual group and the application of characters in Fourier series. At the end, there is a interesting discussion about the determinants of finite abelian groups.