When you delete a group, references are removed from the group but are not deleted; the references themselves are still part of the library.
Temporary groups are always removed when you close the library.
When you delete an Online Search group, it does not mean that you can no longer search that online database. You have not deleted the connection file, but you have removed it as a favorite. You can go to Tools Online Search and select that connection file again.
To delete a group:
In the left panel of the Library window, click on the name of the group you want to delete.
Select the Delete Group command in one of these ways:
From the Groups menu, select Delete Group.
Control+click Right-click with your mouse on the group name to display a context-sensitive menu, and select Delete.
The group is deleted from the library, but the references that were in the group are still part of the library.