The key idea in geometric group theory is to study infinite groups by endowing them with a
metric and treating them as geometric spaces. This applies to many groups naturally …

Abstract Bader, Furman and Sauer have recently introduced the notion of integrable
measure equivalence for nitely-generated groups. is is the sub-equivalence relation of …

We prove that various subgroups of the mapping class group Mod.†/of a surface† are at
least exponentially distorted. Examples include the Torelli group (answering a question of …

We prove that the dimension of any asymptotic cone over a metric space $(X,\rho) $ does
not exceed the asymptotic Assouad-Nagata dimension $\operatorname {asdim} _ {AN}(X) …

In this article, we introduce a new family of groups, called Chambord groups and constructed
from braided strand diagrams associated to specific semigroup presentations. It includes the …

Full residual finiteness growth of a finitely generated group G measures how efficiently word
metric n-balls of G inject into finite quotients of G. We initiate a study of this growth over the …

We generalize the concept of divergence of finitely generated groups by introducing the
upper and lower relative divergence of a finitely generated group with respect to a subgroup …

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 …

For every k⩾ 3 k\geqslant3, we exhibit a simply connected kk‐nilpotent Lie group N k N_k
whose Dehn function behaves like nk n^k, while the Dehn function of its associated Carnot …

Exponentially Distorted Subgroups in Wreath Products Page 1 The Quarterly Journal of
Mathematics, 2024, 75, 1355–1361 doi:https://doi.org/10.1093/qmath/haae048 Advance Access …