Can anyone explain to me the rules of fighting in a ice hockey match, it looks to me like that refs stand by until someone goes to ground, why don't they break it up earlier?

I think they continue to fight until a hockey game breaks out

There's a book by Ross Bernstein called "The Code: The Unwritten Rules of Fighting and Retaliation in the NHL", you should read.

FYI, fighting in the NHL is part of the game.