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SUMMARY:Salvatore Tringali (Hebei Normal University\, China)
DTSTART:20260717T180000Z
DTEND:20260717T182500Z
DTSTAMP:20260710T111632Z
UID:CANT2026/69
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/69/
 ">Power semigroups and two rigidity theorems for groups</a>\nby Salvatore 
 Tringali (Hebei Normal University\, China) as part of Combinatorial and ad
 ditive number theory seminar (CANT 2026)\n\nLecture held in Science Center
  in the CUNY Graduate Center (4th floor).\n\nAbstract\nLet $\\mathcal P(H)
 $ be the semigroup obtained by endowing the family of all non-empty subset
 s of a semigroup $H$ with the setwise operation naturally induced by $H$ o
 n its power set\, and denote by $\\mathcal P_\\text{fin}(H)$ the subsemigr
 oup of $\\mathcal P(H)$ consisting of all non-empty finite subsets of $H$.
  We call $\\mathcal P(H)$ and $\\mathcal P_\\text{fin}(H)$ the large power
  semigroup and the finitary power semigroup of $H$\, respectively.\n\nWe s
 how that if $H$ is a group and $K$ is an arbitrary semigroup\, then for\n$
 \\mathcal P(H)$ to be isomorphic to $\\mathcal P(K)$ it is necessary (and 
 sufficient) that $H$ is isomorphic to $K$ (and hence $K$ is itself a group
 ). The finitary\nanalogue of the same statement appears to be considerably
  more difficult\,\nand we establish it only when $H$ is an additive subgro
 up of the\nrationals. The proof of this second result\nrelies\, in a circu
 itous way\, on a special case of the Evertse--Schlickewei--Schmidt\ntheore
 m. The talk is based on joint work with Shuolin Liu.\n
LOCATION:https://researchseminars.org/talk/CANT2026/69/
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