The Automorphism Group of the Finitary Power Monoid of the Integers under Addition
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917987717480448 |
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| author | Tringali, Salvatore Wen, Kerou |
| author_facet | Tringali, Salvatore Wen, Kerou |
| contents | Endowed with the binary operation of set addition carried over from the integers, the family $\mathcal P_{\mathrm{fin}}(\mathbb Z) $ of all non-empty finite subsets of $\mathbb Z$ forms a monoid whose neutral element is the singleton $\{0\}$.
Building upon recent work by Tringali and Yan, we determine the automorphisms of $\mathcal P_{\mathrm{fin}}(\mathbb Z)$. In particular, we find that the automorphism group of $\mathcal P_{\mathrm{fin}}(\mathbb Z)$ is isomorphic to the direct product of a cyclic group of order two by the infinite dihedral group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Automorphism Group of the Finitary Power Monoid of the Integers under Addition Tringali, Salvatore Wen, Kerou Combinatorics Group Theory Number Theory Primary 08A35, 11P99. Secondary 20M13 Endowed with the binary operation of set addition carried over from the integers, the family $\mathcal P_{\mathrm{fin}}(\mathbb Z) $ of all non-empty finite subsets of $\mathbb Z$ forms a monoid whose neutral element is the singleton $\{0\}$. Building upon recent work by Tringali and Yan, we determine the automorphisms of $\mathcal P_{\mathrm{fin}}(\mathbb Z)$. In particular, we find that the automorphism group of $\mathcal P_{\mathrm{fin}}(\mathbb Z)$ is isomorphic to the direct product of a cyclic group of order two by the infinite dihedral group. |
| title | The Automorphism Group of the Finitary Power Monoid of the Integers under Addition |
| topic | Combinatorics Group Theory Number Theory Primary 08A35, 11P99. Secondary 20M13 |
| url | https://arxiv.org/abs/2504.12566 |