TIL that you can sign up for Google groups without using Google account. Just send email to email@example.com (notice +subscribe part and - part if there are spaces between), just be sure to send it from email account you want to recieve emails to. Group email can be found on information about that group
@nikolal why would you want to use Google groups in the first place?? Just asking?
@Wetrix alas some communities (still) use gratis mailing lists provided by Google
e.g. from top of my head https://groups.google.com/forum/#!forum/appliedcategorytheory or https://groups.google.com/forum/#!forum/clash-language
Local foss community uses it, I just subscribe to mailing list which is on g groups