Ashley J Gittins
Getting a bit off-topic here, but I am pretty sure that none of the things you said there are true.
Google was founded in 1996 by Larry Page and Sergey Brin, who, along with Scott Hassan (actually, mostly the latter) wrote the google search engine. Yahoo's search engine was not part of that lineage.
Maybe you are confused because Yahoo signed a search deal with google in 2000, so from then Yahoo showed google search results on their site. This is after they dropped using inktomi, the search provider behind hotbot/lyca et al who they were using prior to that for search results (they later bought inktomi in 2006).
Yahoo are leaving the groups space because they don't see value in it - just like they left search, just like they left geocities, just like they left delicious, and yahoo messenger, and all sorts of other products they've let go along the way. Sure, competing with google is tough, but yahoo's not some poor victim here, and it sure isn't the creator of what made google special. Yahoo for a loooong time has been a media company, not a tech company.