# Finite groups acting on compact complex parallelizable manifolds

## TL;DR

This paper proves that the automorphism groups of compact complex parallelizable manifolds are Jordan groups, and shows that outer automorphism groups of cocompact lattices in complex Lie groups have bounded finite subgroups.

## Contribution

It establishes the Jordan property for automorphism groups of these manifolds and bounds finite subgroups of certain lattice automorphism groups, advancing understanding of their structure.

## Key findings

- Automorphism groups of compact complex parallelizable manifolds are Jordan.
- Outer automorphism groups of cocompact lattices in complex Lie groups have bounded finite subgroups.
- Provides structural insights into automorphism groups in complex geometry.

## Abstract

We prove that the automorphism group of a compact complex parallelizable manifold is Jordan. In the course of the proof we show that outer automorphism groups of cocompact lattices in complex Lie groups have bounded finite subgroups.