How did the soviet union maintain control of east germany after world war ii?

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.

c. extended rights of citizenship to new groups