Thick Difference Sets of Haar Null Compact Sets in Locally Compact Groups
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910082287009792 |
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| author | Akemann, Chuck |
| author_facet | Akemann, Chuck |
| contents | Let \(G\) be a non-discrete, locally compact group with Haar measure \(m\). We prove that there exists a compact set \(K \subset G\) with \(m(K)=0\) such that \(KK^{-1}\) contains a neighborhood of the identity. Moreover, such a set may be constructed inside any prescribed neighborhood of the identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27479 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thick Difference Sets of Haar Null Compact Sets in Locally Compact Groups Akemann, Chuck Group Theory 22C05 (Primary) Let \(G\) be a non-discrete, locally compact group with Haar measure \(m\). We prove that there exists a compact set \(K \subset G\) with \(m(K)=0\) such that \(KK^{-1}\) contains a neighborhood of the identity. Moreover, such a set may be constructed inside any prescribed neighborhood of the identity. |
| title | Thick Difference Sets of Haar Null Compact Sets in Locally Compact Groups |
| topic | Group Theory 22C05 (Primary) |
| url | https://arxiv.org/abs/2603.27479 |