APLIKASI ARITMATIKA MODULAR DALAM PENGKLASIFIKASIAN KELAS KONJUGASI GRUP DIHEDRAL 𝑫𝟐�

Authors

  • Nugraha Kristiano Floresda Dethan Universitas Timor
  • Faustianus Luan Universitas Timor

DOI:

https://doi.org/10.32493/sm.v4i1.20408

Keywords:

Aritmatika modular, Grup dihedral, Kelas konjugasi

Abstract

Misalkan ðºð¿2 (â„) = {ð´ = [ ð‘Ž11 ð‘Ž12 ð‘Ž21 ð‘Ž22 ]: ð‘Žð‘–𑗠∈ â„, ð‘‘ð‘’ð‘¡(ð´) ≠ 0}. Maka jelas bahwa 𜎠= [ ð‘ð‘œð‘ (2ðœ‹/ð‘›) ð‘ ð‘–ð‘›(2ðœ‹/ð‘›) −ð‘ ð‘–ð‘›(2ðœ‹/ð‘›) ð‘ð‘œð‘ (2ðœ‹/ð‘›) ] dan ðœ = [ 1 0 0 −1 ] merupakan dua elemen dari ðºð¿2 (â„). Grup dihedral merupakan grup simetri dari poligon beraturan dengan ð‘› sisi yang dibangkitkan oleh 𜎠dan ðœ. Telah dilakukan suatu kajian terhadap klasifikasi kelas konjugasi dari grup dihedral ð·2ð‘› dengan menggunakan arimatika modular. Tulisan ini membahas dan membuktikan beberapa sifat dasar arimatika modular, grup dihedral, kelas konjugasi, dan kemudian kelas konjugasi untuk grup dihedral secara khusus. Hasil yang diperoleh dari kajian ini adalah terdapat tiga jenis kelas konjugasi pada grup dihedral ð·2ð‘› untuk ð‘› ganjil dan empat jenis kelas konjugasi pada grup dihedral ð·2ð‘› untuk ð‘› genap.

Author Biography

Faustianus Luan, Universitas Timor

Program Studi Matematika, Universitas Timor

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Published

2022-01-31

Issue

Vol. 4 No. 1 (2022)

Section

Articles

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