An uncountable family of finitely generated residually finite groups

Abstract

We study a family of finitely generated residually finite groups. These groups are doubles F 2 * H F 2 F_{2}*_{H}F_{2} of a rank-2 free group F 2 F_{2} along an infinitely generated subgroup 𝐻. Varying 𝐻 yields uncountably many groups up to isomorphism.

Continuously many quasi-isometry classes of residually finite groups

“…We also produced an uncountable family of pairwise non-isomorphic residually finite groups in [3], and perhaps an appropriate subfamily also yields continuously many quasi-isometry classes.…”