Orde Subgrup Terkecil yang Memuat Suatu Himpunan dengan 2 Unsur dari Suatu Grup Hingga Siklik

Rasdin Sandria, Jufra Jufra, Norma Muhtar

Abstract


Suppose is any group and then the smallest subgroup of containing is the intersection of all subgroups of containing and denoted by . If then , such a subgroup we know as a cyclic group with generator , such that the order of is the same as the order of . In this research, observations were made on the set in order to know the nature of the membership of and the order of for the case of order 2 and further for of order n if G is a cyclic finite group using the effect of Lagrange Theorem.

Keywords


Smallest Subgroup, Lagrange Theorem, Order, Cyclic Group, Finite Group

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DOI: https://doi.org/10.15548/jostech.v3i1.5667
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References


Shadiq, F. Pembelajaran Matematika (Cara Meningkatkan Kemampuan Berpikir Siswa). Yogyakarta: Graha Ilmu, 2014.

Sinaga, W., B. H. Parhusif, R. Tarigan, and S. Sitepu, “Perkembangan Matematika dalam Filsafat dan Aliran Formalisme yang Terkandung dalam Filsafat Matematika.” SEPREN : Journal of Mathematics Education and Applied, vol. 2, no. 2, pp. 17-22, 2021.

Rahayu, Annisa Melinia, Farid H Badruzzaman, and Erwin Harahap, “Pembelajaran Aljabar Melalui Aplikasi Wolfram Alpha.” Jurnal Matematika, vol. 20, no. 1, pp. 51-58, 2021.

Anggraini, and G. Sugita. Buku Ajar Struktur Aljabar. Sleman: Deepublish, 2020.

Herstein, I. Nathan. Abstract Algebra, 3rd edition. New Jersey: Prentice-Hall, 1996.

Roman, S. Fundamentals of Group Theory: An Advanced Approach. New York: Birkhauser, 2011.

Hungerford, T. William. Abstract Algebra: An Introduction, 3rd edition. Boston: Cengange Learning, 2012.

Anderson, Marlow., and Todd Feil. A First Course in Abstract Algebra: Rings, Groups, and Fields, 2nd edition. Florida: Chapman & Hall/CRC Press, 2004.

Humphreys John F.. A Course in Group Theory. New York: Oxford University Press, 1996.

Saracino, D. Abstract Algebra: A First Course. 2nd edition. Illinois: Waveland Press Inc, 2008.

Dummit, David S., and Richard M. Foote. Abstract Algebra, 3rd edition. New Jersey: John Wiley & Sons, 2003.

Fraleigh, J. B. A First Course in Abstract Algebra: Pearson New International Edition, 7th edition. London: Pearson Education Limited, 2013.

Gallian, Joseph A.. Contemporary Abstract Algebra, 9th edition. Boston: Cengange Learning, 2015.

Adhikari, Mahima R., and Avishek Adhikari. Basic Modern Algebra with Applications. India: Springer, 2014.

Lal, Ramji. Algebra 1: Groups, Rings, Fields and Arithmetic. Singapore: Springer, 2017.


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