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SUMMARY:Salvatore Tringali (Hebei Normal University\, China)
DTSTART:20250523T130000Z
DTEND:20250523T132500Z
DTSTAMP:20260423T010101Z
UID:CANT2025/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/7/"
 >Power monoids and the Bienvenu-Geroldinger problem for torsion groups</a>
 \nby Salvatore Tringali (Hebei Normal University\, China) as part of Combi
 natorial and additive number theory (CANT 2025)\n\nLecture held in CUNY Gr
 aduate Center - Science Center (4th floor).\n\nAbstract\nLet $M$ be a (mul
 tiplicatively written) monoid with identity element $1_M$.  \nEndowed with
  the operation of setwise multiplication induced by $M$\, the collection \
 nof finite subsets of $M$ containing $1_M$ forms a monoid in its own right
 \, denoted \nby $\\mathcal{P}_{\\mathrm{fin}\,1}(M)$ and called the reduce
 d finitary power monoid of $M$.\n \nIt is natural to ask whether\, for all
  $H$ and $K$ in a given class of monoids\, \n$\\mathcal{P}_{\\mathrm{fin}\
 ,1}(H)$ is isomorphic to $\\mathcal{P}_{\\mathrm{fin}\,1}(K)$ \nif and onl
 y if $H$ is isomorphic to $K$. Originating from a conjecture of Bienvenu a
 nd \nGeroldinger recently settled by Yan and myself\, the problem --- toge
 ther with its numerous \nvariants and ramifications --- has non-trivial co
 nnections to additive number theory and related fields.\nIn this talk\, I 
 will present a positive solution for the class of torsion groups.\n
LOCATION:https://researchseminars.org/talk/CANT2025/7/
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