Trying to figure out how the search works on Facebook isn’t easy, so here’s a couple of neat links that might help:
Blog #1: Facebook’s search algorithm is the most bizarre search algorithm known to man.
Blog #2: How a corporate can grab back a fan page on FB, using the coca cola example.

I've deactivated my Facebook account
Finally (08 Apr 09) received this response on how groups are ranked via a colleague’s LinkedIn Facebook group:
“To the best of my knowledge Facebook haven’t released the ranking algorithm, but it looks like the title of the group plays a big part, with things like the description helping as well. I guess it’s similar to basic on site optimisation. Put the keyword in the title, the description etc.”