In Zotero, a library can belong to a group:
One person in your group should create a group library and INVITE the other group members to join. To invite, be sure to use the email addresses they used to sign up to Zotero for the invite.
Save your references into the group library.
When you sync to the Zotero server, the reference you added will be uploaded to the Zotero server. When the other group members sync, that reference will show up in the group library folder in their Zotero library as well.