Basis dari grup dihedral

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 (Unpublished)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)
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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