These notes consist of six sections. In the first three we introduce some classical results in several directions. In fourth section se develop isoperimetric tools for torsion-free groups and provide several very short proofs using the new technique. In fifth section we extend notions and main lemmas for general groups and provide proofs for theorems stated in the first sections. In last section we provide several observations, conjectures and recent results in the area.


Abelian Group Nonempty Subset Cayley Graph Arithmetic Progression Short Proof 
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© Birkhäuser Verlag 2009

Authors and Affiliations

  • Yahya O. Hamidoune
    • 1
  1. 1.E.Combinatoire-case 189Université Pierre et Marie Curie (Paris 6)Paris Cedex 05France

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