I would say that group violence is channeling the violence of individuals to achieve some goal a group might have.

Chimp Empire is worth watching in this context.

The most basic definition of state is that it is some institution with the monopoly of violence. Think of it, who in all myriad society organisations and hierarchies has the legitimacy to use force? The state. Even murder is allowed and trained for, if you are part of the state organisation, normally called armed forces. Many anarchists in the XIX century despised the idea of state because accepting it means accepting organised violence and importantly a monopoly on it.

Reaching aaaall the way back to high school, this is basic locke theory of government. You give up a freedom to gain some protection against the jerks who would use that freedom against you.

https://plato.stanford.edu/entries/locke-political/

It does seem to me that most political arguments fall into this category

I would argue that the OG of state violence monopoly is Thomas Hobbes and the concept of sovereign as the deposit of the individual’s ability for violence. Will read the link though. In Portugal there is also philosophy in high school and with time I realize that it was the most practical and important class I ever had and at the time me and my colleagues completely missed its value.

There is a book about this.

https://en.wikipedia.org/wiki/Leviathan_(Hobbes_book)