88304am永利集团

主 讲 人 ：Balint Rago    

活动时间：2025-09-21 17:10:00

地      点 ：数学科学学院D203报告厅(Zoom: https://us06web.zoom.us/j/86763384947?pwd=qXhOzOcHvaaiw2jqADI8iqNavdgm14.1, ID: 86763384947; passcode: 612593)

主办单位：数学科学学院

讲座内容：

Let $H$ be a multiplicatively written monoid. The family $\mathcal{P}_{{\rm fin},1}(H)$ of non-empty finite subsets of $H$ containing the identity, endowed with the binary operation of setwise multiplication $(X,Y) \mapsto \{xy: x \in X, y \in Y\}$ induced by $H$, is called the reduced finitary power monoid of $H$. Recently, Tringali and Yan initiated the investigation of the automorphism group of these objects and showed that the reduced finitary power monoid of the monoid $\mathbb N_0$ of non-negative integers under addition has precisely two automorphisms, the identity and the so-called reversion map. The existence of the latter is interesting in the sense that it is not the canonical extension of an automorphism of the base monoid $\mathbb{N}_0$.

In this talk, we give a complete description of the automorphism group of $\mathcal{P}_{{\rm fin},1}(H)$, where $H$ is either a finite abelian group or a submonoid of the additive group of rational numbers. More precisely, we show that there is a canonical isomorphism between the automorphism group of $\mathcal{P}_{{\rm fin},1}(H)$ and the automorphism group of $H$, except in certain special cases.

主讲人介绍：

Balint Rago is a 4th-year PhD student in the Discrete Mathematics Consortium of the Doctoral Academy at the University of Graz (Austria). His research focuses on commutative ring theory and factorization theory, with a recent interest in the study of power semigroups and power monoids. Some of his results have been published in journals such as Proc. Amer. Math. Soc., Pacific J. Math., and Acta Arith.