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.
1
Hawaii Pacific University, Honolulu, USA
2
Vanderbilt University, Nashville, United States
Tara C. Davis; Alexander Yu. Olshanskii. Relative subgroup growth and subgroup distortion. Groups, geometry, and dynamics, Tome 9 (2015) no. 1, pp. 237-273. doi: 10.4171/ggd/312
@article{10_4171_ggd_312,
author = {Tara C. Davis and Alexander Yu. Olshanskii},
title = {Relative subgroup growth and subgroup distortion},
journal = {Groups, geometry, and dynamics},
pages = {237--273},
year = {2015},
volume = {9},
number = {1},
doi = {10.4171/ggd/312},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/312/}
}
TY - JOUR
AU - Tara C. Davis
AU - Alexander Yu. Olshanskii
TI - Relative subgroup growth and subgroup distortion
JO - Groups, geometry, and dynamics
PY - 2015
SP - 237
EP - 273
VL - 9
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/312/
DO - 10.4171/ggd/312
ID - 10_4171_ggd_312
ER -
%0 Journal Article
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%A Alexander Yu. Olshanskii
%T Relative subgroup growth and subgroup distortion
%J Groups, geometry, and dynamics
%D 2015
%P 237-273
%V 9
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/312/
%R 10.4171/ggd/312
%F 10_4171_ggd_312
