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Title 
Lie Methods in Growth of Groups and Groups of Finite Width 

Authors  
Published in  Computational and geometric aspects of modern algebra. Edinburgh  1998  Cambridge: Cambridge University Press. 2000  
Collection 
London Mathematical Society lecture note series; 275 

Abstract  In the first, mostly expository, part of this paper, a graded Lie algebra is associated to every group G given with an Nseries of subgroups. The asymptotics of the Poincare series of this algebra give estimates on the growth of the group G. This establishes the existence of a gap between polynomial growth and growth of type $e^{sqrt n}$ in the class of residuallyp groups, and gives examples of finitely generated pgroups of uniformly exponential growth. In the second part, we produce two examples of groups of finite width and describe their Lie algebras, introducing a notion of Cayley graph for graded Lie algebras. We compute explicitly their lower central and dimensional series, and outline a general method applicable to some other groups from the class of branch groups. These examples produce counterexamples to a conjecture on the structure of justinfinite groups of finite width.  
Identifiers  arXiv: math/0002010v2  
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Citation (ISO format)  BARTHOLDI, Laurent, GRIGORCHUK, Rostislav. Lie Methods in Growth of Groups and Groups of Finite Width. In: Computational and geometric aspects of modern algebra. Edinburgh. Cambridge : Cambridge University Press, 2000. (London Mathematical Society lecture note series; 275) https://archiveouverte.unige.ch/unige:12438 