It appears that your mapping is incorrect.
You have a navigation property because
It must be added in the mapping in the following manner:
modelBuilder.Entity<Person>() .HasOptional(t => t.Group) .WithMany(t => t.People) // <--- .HasForeignKey(t => t.GroupId);
If not, EF will construct a new foreign key and utilize the navigation property to establish a different relationship between the two entities.