The automorphism group of reduced power monoids of finite abelian groups

Balint Rago

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arXiv · 2510.17533

The automorphism group of reduced power monoids of finite abelian groups

Balint Rago

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Abstract

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.

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Balint Rago. 2025-10-20. The automorphism group of reduced power monoids of finite abelian groups. https://arxiv.org/abs/2510.17533

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