We call a group G very Jordan if it contains a normal abelian subgroup G such that the orders of finite subgroups of the quotient G/ G are bounded by a constant depending on G only. Let Y be a complex torus of algebraic dimension 0. We prove that if X is a non-trivial holomorphic P1-bundle over Y then the group Bim (X) of its bimeromorphic automorphisms is very Jordan (contrary to the case when Y has positive algebraic dimension). This assertion remains true if Y is any connected compact complex Kähler manifold of algebraic dimension 0 without rational curves or analytic subsets of codimension 1.
All Science Journal Classification (ASJC) codes