Believe it or not, we learned this JUST TODAY. We've no idea how we overlooked it!
If you select EDIT > GROUPS and choose INFO for the group you want, you can uncheck a box that will stop you from receiving group notices.
Similarly, you can uncheck the box that says List Groups in My Profile, and no one will be able to see you are in the group Notrious Uncaught Serial Killers Looking for Victims in Virtual Worlds.
On second thought, maybe you'd better leave that box checked! :p