How does abigail williams in the crucible influence the other girls?

Abigail's parents were killed. She receives no affection from Parris other than material needs. She finally does find affection from John Proctor. When she and the other girls conspire to make up the story about witchcraft, she and the girls are trying to stay out of trouble, but this could also be another of Abigail's attempts to get attention (good or bad) and/or affection from someone. Keep in mind that she lives in a Puritan village, a very religious place where affection is strictly regulated and passion is reserved for devotion to God. Consequently, she seeks affection in any way she can. 

That being said, she can not be totally excused from the hysteria she helped create. The question is how does she exert power over the other girls. One answer is that because she feels so alone, she will do whatever it takes to get attention. The girls fall victim to Abby's determination and find it difficult to disagree with her because she seems so confident.