First, I think you need to rethink a few things. You did not cheat on your boyfriend. At the time you slept with the other guy, you were single and trying to move on from an abusive relationship. Don't let him make you think you cheated.

Next, has he taken actions about his abusive behavior? Has he started any sort of anger management classes or therapy? I think those things are paramount to the success of your relationship. Furthermore, I think he is being emotionally abusive to you right now (another reason he should be going to therapy). Honestly, in my opinion, I think you should tell him he needs to stop verbally beating you up over this one night when you were single, or you won't be sticking around. If you would really like to stay with him, offer to go to therapy with him to help him move past this, but don't let him tell you you cheated. If he wants to make this relationship work, then he has to prove it to you. No more abuse, no more name calling, no more saying you cheated, no more involving other people, and definitely, no more bring up the past. Then stick to your guns.

I hope I didn't come off as harsh, but you deserve better than this.
Good luck