It is possible to allow members into a group from outside the Beloit College domain (beloit.edu). To do so follow the instructions given below.
Navigate to your group in Google Groups.
Click on the gear/settings icon.
On the context menu, click Group Settings
Expand the Settings menu item on the left side of the screen.
Click on Identity.
Check the box to Either display name or Google profile for the Required Forms of Identity. It is also recommended that you check the box to Every display name must be unique.
Click on the Save button.
Now navigate to and expand the Permissions menu. Click on Basic Permissions.
Check the box to, Allow new users not in beloit.edu.
Save the changes. You can now navigate toMembers > Direct add membersand enter the email addresses or the members outside the Beloit College domain you would like to add to the group.