Stupid Schmuckerberg... and the horse he rode in on.
if they are successful in getting you to download the keylogger, they then have access to everything that you do on that particular computer.
Other scams on FB include scammers cloning your "friends" then sending you invites likely so they can eventually infect your computer with key loggers to obtain your usernames/pw's on the sites you go to.
Indeed facebook is a serious security issue and a prime cause of identity theft. For this reason I do not have a Facebook account. Scammers love Facebook, because it is an apparently endless repository of easily stolen identities, personal details and pictures. Most scam victims I talked to (and this is quite a few) were scammed from Facebook, and some from other dating sites and its various iterations. The same company also owns a Muslim dating site. Premium dating sites are therefore NOT safe to use despite implied security.
Wanted to share it - facebook don't police their site at all...