Near-factorizations of dihedral groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916586240081920 |
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| author | Kreher, Donald L. Paterson, Maura B. Stinson, Douglas R. |
| author_facet | Kreher, Donald L. Paterson, Maura B. Stinson, Douglas R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Near-factorizations of dihedral groups Kreher, Donald L. Paterson, Maura B. Stinson, Douglas R. Group Theory Combinatorics 05B10 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. |
| title | Near-factorizations of dihedral groups |
| topic | Group Theory Combinatorics 05B10 |
| url | https://arxiv.org/abs/2411.15884 |