A group invitation will include a link to the group, which will show buttons to accept or decline.
If those buttons aren't showing up, or aren't functioning, your browser or an extension may be blocking the javascript on the page from running.
Invitations that were sent to your existing Zotero account, or to a verified email address associated with your account, will also show up on your groups page (https://www.zotero.org/groups).
The buttons would also not show up if you're already a member of the group (the group would then show up on your groups page) or if the invitation had been deleted by the group admin before you accepted it.
You would need to describe what you're seeing for us to tell you more.
If you received an emailed group invitation but you don't see the buttons when you follow the link, you can forward it to support@zotero.org and we can tell you more.
I have invited two colleagues to join. Both of them have downloaded the application and attempted to register. They do not get the buttons. Both have Javascript working.
There are two invitations pending for your group. One of them appears to be for an alternative email of yours, which would not do anything while you're logged in to an account that's already in the group.
The other invitation should show up on the right side of https://www.zotero.org/groups/ for the user if they are logged in to their account.
This is done in a browser on zotero.org, not the Zotero application.
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If those buttons aren't showing up, or aren't functioning, your browser or an extension may be blocking the javascript on the page from running.
Invitations that were sent to your existing Zotero account, or to a verified email address associated with your account, will also show up on your groups page (https://www.zotero.org/groups).
You would need to describe what you're seeing for us to tell you more.
If you received an emailed group invitation but you don't see the buttons when you follow the link, you can forward it to support@zotero.org and we can tell you more.
The other invitation should show up on the right side of https://www.zotero.org/groups/ for the user if they are logged in to their account.
This is done in a browser on zotero.org, not the Zotero application.