Groups provide a method to collaborate with other Zotero users. There are three different types of groups.
When you click on the Create New Group button in the Zotero tab, you will be brought to this page on Zotero's website which will give you the ability to create groups of different sorts:
Groups provide a method to collaborate with other Zotero users. There are three different types of groups. Unless there is an explicit reason for not selecting the Private group type, the Private type seems the best suited for most uses.
Public, Open Membership: Open public groups are useful for the broadest discussion and collaboration. The group page is public, and anyone who wants to can join instantly. If the group has a public library, administrators can choose to show or hide the entire library or individual collections from non-members.
Public, Closed Membership: Closed-membership groups are useful for creating a controlled group environment with a public presence. This allows a group to publicly present its work and sources, or develop new membership in a controlled fashion. Anyone can view the group page, but the only way to join the group is by invitation or by requesting an invitation. If the group has a public library, administrators can choose to show or hide the entire library or individual collections from non-members
Private Membership: Private groups provide a means of collaboration among group members without creating any public face for the group online. Only group members and users invited to join the group are able to see the group’s page. Private groups are completely hidden from group searches. They are not shown on members’ public profile pages and will not appear in search engine results.
Once you've created a group for your project, you need to invite members. To do so, go to the Zotero website, click on the Groups tab and then on the "Manage Members" link. On this page there is a link that will allow you to invite users, so be sure to have the emails they used to create their Zotero accounts handy!
The settings to manage who can edit the group's library and edit file attachments is located on Zotero's website under Groups, then the group you're using, then Library Settings, then Library Editing and File Editing. Like so:
There are two main options available here:
The most likely reason for this is that the owner of the group has filled up their quota of free space. The owner of the group can check on this by going to Zotero's website, logging in, clicking Settings, then selecting Storage. It will take you to this page: https://www.zotero.org/settings/storage. The page will look similar to this:
If they have used up all of their storage, then they have two options: