I understand that you're looking for a way to control user access to content within a social group. Unfortunately, permissions in a social group function different than in a space. This is explained in detail here:
In summary, a social group allows all members to participate as collaborative peers, so this means any member will be able to edit content, with exception to comments. If defined permissions are preferred, I would recommend moving the content over to a space.
I hope this helps. Let me know if you had any remaining questions on this.