%0 Journal Article
%T On the dimension growth of groups
%A Alexander Dranishnikov
%A Mark Sapir
%J Mathematics
%D 2010
%I arXiv
%X Dimension growth functions of groups have been introduced by Gromov in 1999. We prove that every solvable finitely generated subgroups of the R. Thompson group $F$ has polynomial dimension growth while the group $F$ itself, and some solvable groups of class 3 have exponential dimension growth with exponential control. We describe connections between dimension growth, expansion properties of finite graphs and the Ramsey theory.
%U http://arxiv.org/abs/1008.3868v4