  The classical archipelago is a non-contractible subset of $\mathbb{R}^3$
which is homeomorphic to a disk except at one non-manifold point. Its
fundamental group, $\mathcal{A}$, is the quotient of the topologist's product
of $\mathbb Z$, the fundamental group of the shrinking wedge of countably many
copies of the circle (the Hawaiian earring), modulo the corresponding free
product. We show $\mathcal{A}$ is locally free, not indicable, and has the
rationals both as a subgroup and a quotient group. Replacing $\mathbb Z$ with
arbitrary groups yields the notion of archipelago groups.
  Surprisingly, every archipelago of countable groups is isomorphic to either
$\mathcal{A}(\mathbb Z)$ or $\mathcal{A}(\mathbb Z_2)$, the cases where the
archipelago is built from circles or projective planes respectively. We
conjecture that these two groups are isomorphic and prove that for large enough
cardinalities of $G_i$, $\mathcal{A}(G_i)$ is not isomorphic to either.
