Facebook – How to stop Facebook from suggesting the friends join the closed Facebook groups

It looks like this is currently somewhat broken.
If you go to an existing group (Aleph-One Strong for the Generalized Continuum Hypothesis!), then click on the category in the information, it takes you to a link which appears to be a search link (Outlandish Statements from the above group), but it gives you the message "Please enter a query." If you then put in a search term, it searches among all groups.

However, if you add &q=searchterm to the link, you get a search for your searchterm in your category. Taking the example from above, http://www.facebook.com/search.php?sfxp=1&c1=10&c2=141&type=groups&q=answer will get you a list of all groups in the category "Outlandish Statements".

With the millions of groups, and small number of categories for groups, a list of all groups in a category would be too large to look through them.

You can't prevent people from adding you to groups - you can only leave a group once added.

See this Facebook article

Can I prevent people from adding me to a new group?

The functionality of approving a group membership is not available. Similar to being tagged in a photo, you can only be added to a group by one of your friends. When a friend adds you to a group, a story in the group (and in News Feed for Open or Closed groups) will indicate that your friend has added you to a group.

Please keep in mind:

• Only your friends can add you to groups.
• When a friend adds you to a group, you'll get a notification right away.
• You can leave a group anytime. To do so, just go to the group page and click "Leave Group" in the right-hand column. Once you leave a group, you can't be added by anyone else unless you explicitly request to be re-added