Alright, so the need to be introduced by someone else actually is a very real thing? Anyway Gamma and Beta seems to be the opposite of you guys. Gammas introduce themselves to people on their own initiative and Betas actively invite others to participate in group activities. To me that is social inclusion.
The way I perceive it, newcomers can actually invite themselves to become accepted in a Beta group. This is because Beta groups often come together around some kind of activity where participation is voluntary and gives outsiders an opportunity to both join in and to be accepted.