Finite groups acting on compact complex parallelizable manifolds

A complex manifold $X$ is called parallelizable if its holomorphic tangent bundle is trivial. A classical theorem of H.-C. Wang says that a compact complex parallelizable manifold is isomorphic to a quotient of a connected complex Lie group by a discrete cocompact subgroup. In my talk I will discuss automorphism groups of compact complex parallelizable manifolds from the viewpoint of their finite subgroups. In particular, I will show that these finite subgroups are “almost abelian” (Jordan property for $\mathrm{Aut}(X)$) and examine some related questions from group theory.