Should schools more closely monitor peer groups?

I was recently watching a special, where a school was coming under heat for a fight that happened there. The fight happened, within one peer group. It appears one girl was kicked out, and retaliated by jumping three group members with her sisters. One girl was rushed to the hospital. However, the other two were able to walk home. This was not the first time the peer group had caused trouble, and this all happened right outside school property.

All this raises my question should schools monitor peer groups more closely? I believe, schools should not monitor the groups more closely just better. Schools could stop a lot of violence and harassment by doing simple things. Simple things such as teachers being active in the children's lives, kepping their ears' open, and listening to the students. Then, the teachers can know about problems in advance, or be there when the problem is happening. However, schools should constantly monitor groups that cause problems. This could be done with weekly counselor visits or by asking peers what the groups are doing.