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