Read-only and single-post

Having an option to make only a single node of a content type possible to create in each group would be very useful.

What I would like is an information-style page per group that only the group admin can add/edit, and limit that to a maximum of one per group. Is this something that is suitable to include in this module? This is what I would like to use this module for, if anyone has an idea of another way to do it, I will be most grateful.