I think that you could send a message to Spamcop in order to describe this issue and get it solved quickly. A friend of mine did it a couple of months ago and it worked.
You should definitely contact Google and explain this situation. After all, as far as I’m concerned, is not exactly normal that you received spams from Google Groups.
First thing first: I’m not an expert at all. Nevertheless, all I can say it is extremely weird what you are describing. After all, Google should definitely use the abuse address.