Group Registerations and Auto Group Members

One of the basic things I wanted is that every registration from a Particular Group page, the person becomes an auto member of that page and once he registers he stays there on that page instead of getting re-directed to the parent site. In simple terms – X lands on group page Y – registers there itself and stays on Y page becoming its auto member.

“Log in” already does this – but not “Register” or “Please create an account to get started”

is this possible?