Aha,
I had to actually click on the group before I could see the option to join or decline. I was looking at it from the first Notifications pane and was hoping to decline without having to go into the group.
My issue was the reverse.
Yesterday, I noticed I had a group invitation pending. It was my first group invite here on EnWorld.
I studied the invitation carefully, searching for the link or button to accept the invite. Nothing was there.
I clicked through to the group, but did not see anything (see below).
I went back to the invite and stared at it a while longer, and still found nothing.
I clicked on Join Social Groups, and then searched for the group, and found my invite again, which did not provide a way to accept the invite.
After about 10 minutes of cycling through this, I started using cntl+f to search for "join" and "accept" on a web page, and finally found a join link at the very bottom of the group's web page, which was a ways down the page and off the screen.
My recommendation: Put join and decline links on the invite. From a human-interface design standpoint, that it where you would expect the options to be. As a second option, perhaps move them somewhere to the top of the group's page where they will be immediately visible upon visiting it.