Kholilurrohman, Mohammad Agus, Wichaksono, Mochamad Bagus Vicky and Ismiarti, Dewi
(2023)
*Basis dari grup dihedral.*
Research Report.
Universitas Islam Negeri Maulana Malik Ibrahim Malang, Malang.
(Unpublished)

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## Abstract

Groups can be considered as a generalization of vector spaces. There are some attempts to develop the concepts of basis from vector spaces to finite groups. Let G be a finite group. A set B of conjugacy classes of G is a basis of G if B is an independent set which generates G. This study aims to determine the bases of dihedral groups. We formulate the bases of dihedral groups D_2n by finding the bases of dihedral groups D_2n for n=3,4,5,6,7,8. Given n∈Z "and" n≥3. If n is odd then the basis of D_2n is {[s]}. Moreover, if n is even then the bases of D_2n are {[r^k ],[s]},{[r^k ],[sr]},{[s],[sr]} where 0≤k≤n/2 and k is odd.

Item Type: | Research (Research Report) |
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Keywords: | bases; dihedral groups; independent sets; conjugacy classes; generating sets |

Subjects: | 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010101 Algebra and Number Theory 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010102 Algebraic and Differential Geometry 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010105 Group Theory and Generalisations 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010199 Pure Mathematics not elsewhere classified |

Divisions: | Faculty of Mathematics and Sciences > Department of Mathematics |

Depositing User: | Dewi Ismiarti |

Date Deposited: | 20 Feb 2024 19:10 |

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