{"id":"hexagon/2610.00148","pdf":"https://hexagonmath.org/pdf/2610.00148v1","url":"https://hexagonmath.org/abs/2610.00148v1","tags":["math.GR","msc:37A25","msc:22D55","msc:20F65"],"score":0,"title":"Uniform Kazhdan Monsters and Schmidt's Property M","domain":"math.DS","origin":"ai-generated","source":"hexagon","authors":["Mehdi Moradi"],"reviews":0,"subject":"math.DS","summary":"Let \\(G\\) be an infinite finitely generated group whose proper subgroups are finite. We prove that a positive Kazhdan constant uniform over all finite generating sets forces every unit vector in every representation without invariant vectors to have a cofinite displacement gap. For ergodic probability-measure-preserving actions this gives \\[ \\liminf_{g\\to\\infty}\\mu(gA\\mathbin\\triangle A) \\geq \\ku(G)^2\\mu(A)(1-\\mu(A)), \\] and hence Schmidt's Property~\\(M\\). A tensor-square argument also gives a uniform gap from modulus one for diagonal matrix coefficients. Conditional on the graded-diagram…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-07","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}