In Zotero you can start your own groups(s) or join existing groups.
You will find three types of groups:
Begin by setting up a group within the program, then invite colleagues to join. You can set up a new group by selecting the “Create a New Group” button on the groups landing page on the Zotero website. You can also set up a new group from Zotero Desktop:
Once you have set up your new group, you will see two sections in your Zotero Desktop left hand collections pane: My Library and Group Libraries. You can drag items back and forth between the two libraries at will.