Okaviananda, Hafidh Dihas (2022) Grup Presentasi. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Suatu grup $G$ dibangun oleh sebarang himpunan $X$, dalam hal ini $G$ me\-rupakan grup bebas terhadap himpunan $X$.
Secara umum, grup bebas $G$ memiliki elemen-elemen yang sama. Dalam hal ini elemen-elemen yang sama dari $G$ dapat direduksi menggunakan suatu relasi $\sim$,
$R=\varnothing$ dengan $R\subseteq G$ sedemikian hingga untuk sebarang elemen $r\in R$ berlaku $r\sim e$ dengan $e\in G$ adalah elemen iden\-titas. Maka $G$ dapat dinyatakan sebagai $G=\left\langle X\mid R\right\rangle $ yang selanjutnya disebut grup presentasi dari $X$. Sedangkan untuk $R=\varnothing$ grup presentasinya merupakan grup bebas. Dalam penelitian ini akan dibahas dan ditelaah pengertian, sifat-sifat, dan teori yang muncul didalam grup presentasi.
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A group G is generated by any set X, in this case G is
a free group on a set X. In general, a free group G has the
same elements. In this case the same elements of G can be
reduced using a relation ∼, with R ⊆ G such that for any
element r ∈ R holds r ∼ e where e ∈ G is the identity
element. Then G can be expressed as G = 〈X | R〉 and it
is called presentation group of X. Meanwhile, for R = ∅ the
presentation group is a free group. In this final project, the
definitions, characteristics, and theories that appear in the
presentation group will be discussed and analyzed.
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | Grup Bebas, Free Group, Grup Presentasi, Presentation group |
| Subjects: | Q Science > QA Mathematics > QA159 Algebra |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Hafidh Dihas Okaviananda |
| Date Deposited: | 11 Feb 2022 03:41 |
| Last Modified: | 01 Nov 2022 03:56 |
| URI: | http://repository.its.ac.id/id/eprint/93667 |
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