We answer in the affirmative a question posed by Ivanov
and Vassilev on the existence of a seven-dimensional
quaternionic contact manifold
with closed fundamental 4-form and non-vanishing
show an approach to the classification of seven-dimensional solvable Lie groups having an integrable left invariant
structure. In particular, we prove that the
unique seven-dimensional nilpotent Lie group admitting such a structure
is the quaternionic Heisenberg group.