The automorphism group of reduced power monoids of finite abelian groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908603439382528 |
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| author | Rago, Balint |
| author_facet | Rago, Balint |
| contents | Let $H$ be an additively written monoid and let $\mathcal{P}_{0}(H)$ denote the reduced power monoid of $H$, that is, the monoid consisting of all subsets of $H$ containing $0$ with set addition as operation. Following work of Tringali, Wen and Yan, we give a full description of the automorphism group of $\mathcal{P}_{0}(G)$, where $G$ is a finite abelian group. More precisely, we show that $\text{Aut}(\mathcal{P}_{0}(G))$ and $\text{Aut}(G)$ are isomorphic in a canonic way, except in the special case when $G$ is isomorphic to the Klein four-group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The automorphism group of reduced power monoids of finite abelian groups Rago, Balint Combinatorics 08A35, 20M14 Let $H$ be an additively written monoid and let $\mathcal{P}_{0}(H)$ denote the reduced power monoid of $H$, that is, the monoid consisting of all subsets of $H$ containing $0$ with set addition as operation. Following work of Tringali, Wen and Yan, we give a full description of the automorphism group of $\mathcal{P}_{0}(G)$, where $G$ is a finite abelian group. More precisely, we show that $\text{Aut}(\mathcal{P}_{0}(G))$ and $\text{Aut}(G)$ are isomorphic in a canonic way, except in the special case when $G$ is isomorphic to the Klein four-group. |
| title | The automorphism group of reduced power monoids of finite abelian groups |
| topic | Combinatorics 08A35, 20M14 |
| url | https://arxiv.org/abs/2510.17533 |