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<p>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.</p>

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Near-factorizations of dihedral groups

  • 期刊论文

  • 发表日期：

    2025年8月16日

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  • Donald L. Kreher,
  • Maura B. Paterson,
  • Douglas R. Stinson

摘要

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.