  We introduce the notion of a meromorphic group, weakening somewhat Fujiki's
definition We prove that a meromorphic group is meromorphically an extension of
a complex torus by a linear algebraic group, generalizing results in [Fujiki,
1978]. A special case of this result, as well as one of the ingredients in the
proof, is that a strongly minimal "modular" meromorphic group is a complex
torus, answering a question of Hrushovski. As a consequence, we show that a
simple compact complex manifold has algebraic and Kummer dimension zero if an
only if its generic type is trivial.
