  A flag domain D = G/V for G a simple real non-compact group G with compact
Cartan subgroup is non-classical if it does not fiber holomorphically or
anti-holomorphically over a Hermitian symmetric space. We prove that any two
points in a non-classical domain D can be joined by a finite chain of compact
subvarieties of D. Then we prove that for F an infinite, finitely generated
discrete subgroup of G, the analytic space F\D does not have an algebraic
structure.
