From my experience running computational research projects between people in my research group (in the UK) and with our collaborators in Singapore we tend to use a few tools.
Sharelatex.com / Dropbox with Latex files: Writing notes for maths is easiest in latex. I'm not sure if you already use it but if not its a mark up language which allows you to easily add mathematical and scientific notation. It is almost exclusively used in the research community and there are a ton of tutorials online. Notes and updates are well presented and easy for others to go through.
Slack: As we are working in collaboration, or in your case studying together, it can be really useful to have a chat space dedicated to the study group. Facebook chat / groups and whatsapp messages proved to be a nightmare for me before and slack is easy to use and free! You can also use the calandar integrations etc.
Speaking Together: Even though we are often based on different continents a voice conversation is infinitely better than just text. Of course this depends on the size of the group but I tend to call my collaborators on a regular basis and they call one another too.
I realise this isnt exactly a study group setting but I think its similar enough?