If Teachernot uploaded, you cannot break the connection. Or include it (eager-load) in the request:
_dataContext.Groups.Include(g => g.Teacher).Single(g => g.Id == groupId);
, , , null:
var teacher = group.Teacher;
group.Teacher = null;
, "Teacher null null", (lazy-load it) , null.
null , group.Teacher = null, ( , , EF , ). , , , Teacher