To see pending applications and approve new group organizers, go to the "Administrators" tab from your group's manage page and go to the pending applications section.
Click the quotation mark icon to see the reason the activist wrote as to why they want to join your group. You can click the mail icon to email them directly using your device's email program so you can have a discussion with them if you want.
If you want to approve them, click the green "Approve" button, otherwise you can decline their application, forcing them to apply again at a later date for access.