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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.10231 |
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| _version_ | 1866917078516105216 |
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| author | Miller, Niklas |
| author_facet | Miller, Niklas |
| contents | We make the observation that certain group automorphisms that fix a large subgroup of an abelian group cannot be multipliers in any non-trivial abelian difference sets, with the single exception of an involution that can be a multiplier in Hadamard difference sets, provided that the difference set contains a sub-difference set of the same type. We use this observation together with a multiplier theorem to rule out the existence of difference sets, and derive bounds for the numerical multiplier group of a difference set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Forbidden multipliers in abelian difference sets Miller, Niklas Combinatorics 05B10 We make the observation that certain group automorphisms that fix a large subgroup of an abelian group cannot be multipliers in any non-trivial abelian difference sets, with the single exception of an involution that can be a multiplier in Hadamard difference sets, provided that the difference set contains a sub-difference set of the same type. We use this observation together with a multiplier theorem to rule out the existence of difference sets, and derive bounds for the numerical multiplier group of a difference set. |
| title | Forbidden multipliers in abelian difference sets |
| topic | Combinatorics 05B10 |
| url | https://arxiv.org/abs/2511.10231 |