There are several resources available for collaborative writing depending on which platform you prefer to work. These are the resources SESYNC groups have successfully used in the past.
For word processing, Google Docs is the most used collaborative platform. Multiple users can work on the platform simultaneously and you can customize group settings and user privileges.
Overleaf allows for multiple users to work in LaTeX. It is free for a single user, but there is a subscription fee to add multiple users. A subscription also allows you to sync with Dropbox and GitHub.
Another free option, HackMD is a great option for working in Markdown. Multiple users can work simultaneously and you can also sync to Dropbox and GitHub to streamline your workflow.
Zotero is a free reference manager. SESYNC can help your group set up a shared library for your project. Google Docs also supports Zotero for creating citations.