Complete decompositions of finite abelian groups

Chin, A. Y. M.; Chen, Huey Voon

doi:10.1007/s00200-018-0371-1

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2019

2023

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Cited by 6 publications

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“…In this paper, we shall focus on investigating the complete decompositions of 2 . In year 2018, the existence of complete decompositions of cyclic group ℤ is determined, refer to [10]. By using the complete decompositions of cyclic groups, they found an application in constructing codes over a binary alphabet.…”

Section: Introductionmentioning

confidence: 99%

On complete decompositions of dihedral groups

Chen

Sin

2021

ITM Web Conf.

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Let G be a finite non-abelian group and B1, …, Bt be nonempty subsets of G for integer t ≥ 2. Suppose that B1, …, Bt are pairwise disjoint, then (B1, …, Bt) is called a complete decomposition of G of order t if the subset product Bi1 … Bit = {bi1 … bit | bij ∈ Bij, j = 1,2, …,t} coincides with G, where {Bi1 … Bit} = {B1, …, Bt} and the Bij are all distinct. Let D2n = ‹r,s| rn = s2 = 1, rs =srn-1› be the dihedral group of order 2n for integer n ≥3. In this paper, we shall give the constructions of the complete decompositions of D2n of order t, where 2 ≤ t ≤ n.

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Section: Introductionmentioning

confidence: 99%