On the automorphisms of numerical power monoids

2026/07/25 by Anwita Bhowmik, Salvatore Tringali
#math.NT #math.CO #math.GR #math.RA

paper · pdf

Abstract

Let H be a numerical monoid, that is, a cofinite submonoid of \mathbb N (the non-negative integers under addition). Denote by \mathcal P_fin,0(H) the monoid obtained by endowing the family of all finite subsets of H containing 0 with the operation of setwise addition induced by H on its power set. Tringali and Yan [JCTA, 2025] have recently established that \mathcal P_fin,0(\mathbb N) has a unique non-trivial automorphism, and conjectured that the automorphism group of \mathcal P_fin,0(H) is trivial whenever H ≠ \mathbb N. We prove this conjecture and, as a byproduct, give a new proof of the Tringali--Yan theorem.

Citations

• On the automorphisms of the power semigroups of a numerical semigroup
• Torsion groups and the Bienvenu–Geroldinger conjecture
• On automorphism groups of power semigroups over numerical semigroups or over numerical monoids
• The automorphism group of reduced power monoids of finite abelian groups
• A counterexample to an isomorphism problem for power monoids
• On the system of length sets of power monoids
• On the arithmetic of power monoids
• On the isomorphism problem for power semigroups
• On algebraic properties of power monoids of numerical monoids

Related

• On the automorphisms of the power semigroups of a numerical semigroup
• On automorphism groups of power semigroups over numerical semigroups or over numerical monoids
• On algebraic properties of power monoids of numerical monoids
• The Automorphism Group of the Finitary Power Monoid of the Integers under Addition
• A counterexample to an isomorphism problem for power monoids