  Six-dimensional N=(1,0) superconformal field theories can be engineered
geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We
include torsional sections in the geometry, which lead to a finite Mordell-Weil
group. This allows us to identify the full non-Abelian group structure rather
than just the algebra. The presence of torsion also modifies the center of the
symmetry groups and the matter representations that can appear. This in turn
affects the tensor branch of these theories. We analyze this change for a large
class of superconformal theories with torsion and explicitly construct their
tensor branches. Finally, we elaborate on the connection to the dual heterotic
and M-theory description, in which our configurations are interpreted as
generalizations of discrete holonomy instantons.
