I like Google Groups a lot, but it's far from perfect. Of all its annoyances, the lack of a killfile (filter) is the biggest.
Fortunately there is a solution for those using Firefox:
3. View one of the offending posts in Google Groups and click on Ignore User. Hooray, now I can finally read melb.general free of all those MI5 Persecution posts! (You can read all about that here, if you wish.)