On a nonabelian Kneser theorem

• Oriol Serra ; Maximilian Wötzel ^[1]
  1. [1] Radboud University, Nijmegen, Netherlands
• Localización: Discrete Mathematics Days 2022 / Luis Felipe Tabera Alonso (ed. lit.), 2022, ISBN 978-84-19024-02-2, págs. 249-254
• Idioma: inglés
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• Resumen

  • The well known theorem of Kneser, stating that small sumsets in abelian groups mustbe periodic, does not hold in nonabelian groups. We prove that in a finite nonabeliangroup G, a weaker version of Kneser’s theorem does hold, stating that if a symmetric set1 ∈ S = S−1 ⊂ G satisfies |S2| < 2|S| − 1 then S2is almost periodic. This is shown in themore general context of vertex transitive graphs. Perhaps surprisingly, the correspondingstatement for infinite vertex transitive graphs turns out to be false.