Near-factorizations of dihedral groups

2024/11/24 by Donald L. Kreher, Kreher, Donald L., Maura B. Paterson +3 · 2 citations
Engineering · Mathematics · #05B10 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Mathematics and Applications #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · doi:10.48550/arxiv.2411.15884

openalex publication_date 2024/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate near-factorizations of nonabelian groups, concentrating on dihedral groups. We show that some known constructions of near-factorizations in dihedral groups yield equivalent near-factorizations. In fact, there are very few known examples of nonequivalent near-factorizations in dihedral or other nonabelian groups; we provide some new examples with the aid of the computer. We also analyse a construction for near-factorizations in dihedral groups from near-factorizations in cyclic groups, due to Pêcher, and we investigate when nonequivalent near-factorizations can be obtained by this method.

Cited by

• On Matrix Product Factorization of Cayley graphs
• Cyclotomic construction of λ-fold near-factorizations of cyclic groups

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