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Groups of Superpolynomial Growth

  • N. Th. Varopoulos

Abstract

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 \( x = \gamma _{{i_1}}^{{ \in _1}}...\gamma _{in}^{{ \in _n}},({i_1},...,{i_n} = 1,...,k;{ \in _j} = 0, \pm 1) \) .

Keywords

Discrete Group Sobolev Inequality Isoperimetric Inequality Dirichlet Form Soluble Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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