On uniform exponential growth for linear groups

@article{Eskin2001OnUE,
  title={On uniform exponential growth for linear groups},
  author={A. Es'kin and S. Mozes and Hee Oh},
  journal={Inventiones mathematicae},
  year={2001},
  volume={160},
  pages={1-30}
}
  • A. Es'kin, S. Mozes, Hee Oh
  • Published 2001
  • Mathematics
  • Inventiones mathematicae
  • Let Γ be a finitely generated group. Given a finite set of generators S of Γ, the word length lS(γ) for an element γ ∈ Γ is defined to be the smallest positive integer for which there exist s1, · · · , sn ∈ S ∪ S −1 such that γ = s1 · · · sn. For each n ∈ N, denote by BS(n) the set of elements in Γ whose word length with respect to S is at most n. It follows from the subadditive property of lS(·) that limn→∞ |BS(n)| 1/n exists, which we denote by ωS(Γ). A finitely generated group Γ is said to… CONTINUE READING
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