Question

How did the Soviet Union maintain control of east Germany after World War II?

Answer 1

I believe the answer is: The soviets kept their troops in east Germany and occupied it

The existence of soviet union troops allow them to influence east germany's political extend. This lead to a situation when there were two opposite ideologies exist in germany.  The eastern Germany that controlled by soviet union adopted a communism ideology while the western Germany that controlled by the Allies adopted a democratic ideology.

Answer 2

There are two main ways the Soviet Union maintain control of east Germany after World War II: through intimidation and violence against the people of East Germany, and be erecting a giant wall (the Iron Curtain) between the east and west.