Relative subgroup growth and subgroup distortion

  • Tara C. Davis

    Hawaii Pacific University, Honolulu, USA
  • Alexander Yu. Olshanskii

    Vanderbilt University, Nashville, United States


We study the relative growth of finitely generated subgroups in finitely generated groups, and the corresponding distortion function of the embeddings. We explore which functions are equivalent to the relative growth functions and distortion functions of finitely generated subgroups. We also study the connections between these two asymptotic invariants of group embeddings. We answer Gromov’s question on the relationship between distortion and connectivity radius functions. We give conditions under which a length function on a finitely generated group can be extended to a length function on a larger group.

Cite this article

Tara C. Davis, Alexander Yu. Olshanskii, Relative subgroup growth and subgroup distortion. Groups Geom. Dyn. 9 (2015), no. 1, pp. 237–273

DOI 10.4171/GGD/312