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 popup menu, click Group Settings
Expand the Settings menu item on the left side of the screen.
Click on Identity.
Under Required Forms of Identity, check the circle next to Either display name or Google profile. It is also recommended that you check the box next 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 next 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.