CHARACTERS OF FINITE ABELIAN GROUPS
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 cha...
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| Format: | Final Project |
| Language: | Indonesia |
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| Online Access: | https://digilib.itb.ac.id/gdl/view/32733 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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