  We prove that the direct sums of extensions of scalars of relation modules
are geometrically realisable as the second homotopy group of a finite
2-complex. We use this to exhibit a finite 2-complex with fundamental group the
$(10,15)$ torus knot group and non-free $\pi_2$, yielding exotic presentations
of a group for which no such examples had previously been known. We conclude by
constructing stably free non-free modules over an infinite family of
Baumslag-Solitar groups; it remains to determine whether these modules are
geometrically realisable by finite 2-complexes.

Algebraic Topology;Group Theory;Geometric Topology;Rings and Algebras