I'm not going to invite a friend's abusive girlfriend to group activities
What is your friend's opinion on the matter?
My friend doesn't seem to mind me not inviting her to our outings, so it's fine.
If your friend doesn't care, then it's no big deal. But you should invite their SO sometimes so they aren't left out.
If she stops being abusive, then sure.
I think you need to talk to your friend about his abusive girlfriend if this is a huge sticking point for you. Continuing to leave her out of outings will only make the situation more awkward.