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All new Google Groups created after April 24, 2010 will have the -groups suffix. Those groups with a suffix of -d (for distribution list) were migrated from PLU's older Distribution List Manager. Those groups with a suffix of -f (for forwarding list) were migrated from PLU's older forwarding lists.
Your group has to be enabled to . Under Group settings, select the Access tab and check the box next to Allow External Members. Once you click the Save Changes button, you will be able to add members to your group who do not have PLU email addresses.
In the older PLU email system, many of the -f groups were created in departmental email accounts, rather than individual email accounts. So if you have access to the password of the departmental account, you can log in to Google Groups with that account and manage your group membership from that account.