It doesn't work, and I know why.
Because I'm using data from multiple tables, you need to define from which table you're selecting. That's why I use 'users AS u' and 'groups AS g'. If I type u.username, it will know it has to look in the table 'users' for the field 'username'. If I don't use it, the database doesn't know where to look for 'username' and thus returns nothing. Same goes for the 'groups AS g' part.
Then why I put WHERE u.group_id = g.group_id. I'm looking in two different tables, which happen to have a record with the same name and value (foreign and primary key as you said). If you don't tell the database that 'u.group_id' is the same as 'g.group_id', it will return everything double. If I add that part though, it will only return it once.
It may look strange, but this is what has to be done in order to get the right data. I get the data I want, in the way I want it, just 'furious' is not ordered by username..
Thanks for the help though