No working trigger functions openHAB 2.1

Items are not required to be a member of a Group. But if you have a Group that has no members then that Group is not doing anything for you nor will that Group ever receive a command or update and therefore cannot be used to trigger a rule (which is how I read your original question/problem).

Groups are useful for far more than the UIs. In truth, their use in the UIs is probably their least useful uses. They can be used to: