My 4yr old is hitting even when there's nothing to frustrate her.?

That one kid picking her a lot might be a bad influence on her. She might be rebellious, but she could also be scared at the same time. Calmly have a talk with her, and ask her if she's having any problems at school that you don't know about. If she is, it might be the cause of her violence. Have a heart-to-heart with her and see if it helps!