Hi,
By default, only owner can add events.
There is a new field to control this. Go to backend -> Groups -> Group Categories and add in a new field called "Event Create". Then head over to frontend and edit the group to set who is allowed to create event within that group.
Also, there is a new field for Group Events that you will have to add at backend -> Events -> Event Categories, called "Member Transfer". This field will determine how should the group member get transferred into group events.