Groups of Superpolynomial Growth

  • N. Th. Varopoulos


Let G be a discrete group generated by a finite number of generators \( {\gamma _1},...,{\gamma _k} \in G. \) . One defines then a distance d(·,·) on G by requiring that d(gx,gy) = d(x, y) (x,y,g € G) and that d(e) x), the distance of x € G from the neutral point e € G is, by definition, the smallest n ≥ 0 for which we can write \( x = \gamma _{{i_1}}^{{ \in _1}}...\gamma _{in}^{{ \in _n}},({i_1},...,{i_n} = 1,...,k;{ \in _j} = 0, \pm 1) \) .


Discrete Group Sobolev Inequality Isoperimetric Inequality Dirichlet Form Soluble Group 
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Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • N. Th. Varopoulos
    • 1
  1. 1.Analyse Complexe et Géométrie (URA 213)Université Paris VIParis cedex 05France

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