If a class of finitely generated groups G is closed under isometric amalgamations
along free subgroups, then every G ∈G can be quasi-isometrically embedded in a
group G∈G that has no proper subgroups of finite index.
Every compact, connected, non-positively curved space X admits an isometric
embedding into a compact, connected, non-positively curved space X such that X
has no non-trivial finite-sheeted coverings.
