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SUMMARY:Neetu (National Institute of Technology Karnataka\, India)
DTSTART:20260717T170000Z
DTEND:20260717T172500Z
DTSTAMP:20260710T111540Z
UID:CANT2026/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/67/
 ">Small doubling in right-ordered groups</a>\nby Neetu (National Institute
  of Technology Karnataka\, India) as part of Combinatorial and additive nu
 mber theory seminar (CANT 2026)\n\nLecture held in Science Center in the C
 UNY Graduate Center (4th floor).\n\nAbstract\nFreiman conjectured that if 
 $S$ is a finite subset of a torsion-free group $G$ with $k\\geq 3$ element
 s and $|S^{2}|\\leq 3k-4\,$ then $S$ is a subset of a small geometric prog
 ression of length at most $2k-3$. In 2014\, Freiman et al. settled this co
 njecture when $S$ is a finite subset of an ordered group. In this talk\, w
 e study this problem in the broader framework of right-ordered groups. Und
 er suitable structural conditions on the subset $S$\, we discuss results t
 hat extend aspects of Freiman's conjecture to this setting. We further foc
 us on the right-ordered Baumslag--Solitar group $$\\text{BS}(1\,q) = \\lan
 gle a\, b \\mid ab = b^q a \\rangle\, \\quad q \\in \\mathbb{Z}.$$ We show
  that for $q \\neq -1$\, if $S$ is a finite subset of $\\text{BS}(1\,q)$ w
 ith the identity element as its minimum and satisfying $|S^2| \\leq 3|S| -
  4$\, then the subgroup generated by $S$ is abelian. This is joint work wi
 th Mohan and B. R. Shankar. The results are based on our recent paper: htt
 ps://link.springer.com/article/10.1007/s00025-025-02576-2.\n
LOCATION:https://researchseminars.org/talk/CANT2026/67/
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