The harmonic archipelago as a universal locally free group

The harmonic archipelago is an important example of a two-dimensional topological space, whose fundamental group displays unusual properties. This group can also be described as a quotient of two different products, a representation somewhat akin to ∏Z/⨁Z, but nonabelian. It is known to be locally free. Here it is shown that every countable locally free group embeds into this fundamental group.