Group administrator only
If someone must be approved by a group admin before they can join the group, they are considered not to be members until their request to join has been approved.
A group administrator can review member requests under the group member list of the relevant group.
The person requesting membership is not sent any information on whether they are accepted or rejected.
Being notified of membership requests
A group administrator can choose to receive an email notification when someone requests to join the group, or when someone joins or leaves a group.
This is set in "Delivery options" on each group's page.