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Home > Volume 2, Number 2, December 2019 > Mahmudi
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Asep Rusyana
Department of Statistics, Faculty of Mathematics and Natural Sciences, Syiah Kuala University
Jalan Syech Abdurrauf No.3, Kopelma Darussalam, Banda Aceh 23111, Aceh, Indonesia
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Beberapa Subgrup dari SL(2,3)

Mahmudi Mahmudi, Ikhsan Maulidi, Saiful Amri

Abstract

Artikel ini membahas mengenai SL(2,3) dengan rincian elemen-elemennya. Dengan bantuan Tabel Cayley dibuktikan bahwa SL(2,3) merupakan grup dan memiliki beberapa subgrup siklik dan subgrup tidak siklik sesuai dengan Teorema Lagrange. Lebih jauh, juga dibuktikan bahwa SL(2,3) tidak memiliki subgrup berorder 12.

This article discusses about SL(2,3)with its detail elements. By using Cayley Table, we prove that SL(2,3)is a group and has cyclic subgroup and noncyclic subgroup according to The Lagrange Theorem. Futher, we also give a detail proof that SL(2,3)has no subgroup of order 12.

 Keywords

Grup SL(2,3); Subgrup Siklik; Tabel Cayley; Teorema Lagrange

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References

J. A. Gallian, Contemporary Abstract Algebra, 9th ed. Boston: Cengage Learning, 2017.

M. Brennan and D. Machale, “Variations on a Theme: A4 Definitely Has no Subgroup of Order Six!,” Math. Mag., vol. 73, no. 1, p. 36, Feb. 2000.

J. B. Nganou, “How rare are subgroups of index 2?,” Math. Mag., vol. 85, no. 3, pp. 215–220, Jun. 2012.

G. Mackiw, “Finite Groups of 2×2 Integer Matrices,” Math. Mag., vol. 69, no. 5, pp. 356–361, 1996.

G. Mackiw, “The Linear Group SL (2, 3) as a Source of Examples,” Math. Gaz., vol. 81, no. 490, p. 64, Mar. 1997.

Shariar Shariari, Algebra in Action, A Course in Groups, Rings, and Fields. Providence, Rhode Island: American Mathematical Society, 2017.

L. Gilbert and J. Gilbert, Elements of Modern Algebra., 8th ed. Stamford: Cengage Learning, 2015.

T. W. Hungerford, Abstract Algebra, an Introduction, Third. Boston: Books/Cole, Cengage Learning, 2014.

M. Mahmudi, “Suatu Catatan tentang Subgrup Normal dan Ideal,” J. Data Analysis, vol. 1, no. 2, pp. 77–82, Dec. 2018.

DOI: https://doi.org/10.24815/jda.v2i2.15788

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About The Authors

Mahmudi Mahmudi
Jurusan Matematika FMIPA Universitas Syiah Kuala

Ikhsan Maulidi
Universitas Syiah Kuala
Indonesia

Jurusan Matematika

Saiful Amri
Universitas Syiah Kuala
Indonesia

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Keywords ARIMA Forecasting Grup SL(2,3) Kesehatan Masyarakat Model Panel Spasial RWikiStat SARIMA SEM Structural Equation Model, Analisis Jalur, Status Gizi Remaja Subgrup Siklik Tabel Cayley Teorema Lagrange acoustic model android iuran normal kewajiban aktuaria metode pendanaan pensiun. neural network pembelajaran statistika projected unit credit speech recognition
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