Fractional isoperimetric inequalities and subgroup distortion

Examples of groups whose automorphisms have exotic growth

“…Other "explicit" examples of distorted elements in a finitely presented group can be found in Gromov [13,Chapter 3] or Bridson [4].…”

Distortion in Free Nilpotent Groups

“…For instance, the complete description of length functions on subgroups of finitely generated and finitely presented groups can be found in [9] and [10]. Other interesting finitely generated groups with fractional distortion are constructed in [3]. Additionally, in [12], the formula for distortion in finitely generated nilpotent groups and nilpotent Lie groups is obtained.…”

Length and Area Functions on Groups and Quasi-Isometric Higman Embeddings

“…Theorem 1 (Bridson,[8]) Let G be a finitely presented group and H ≤ G be a finitely generated subgroup of G with distortion function d(n). Then the Dehn function of the HNN extension…”