Security and Privacy Properties of Groups

I'm curious to understand just how it is that groups work, and what that means for their security and privacy properties. For individual connections, this is all pretty well documented and clear. For groups, it doesn't seem quite as clear to me exactly what compromises or concerns their may be. It also isn't quite clear where groups are built on top of primitives, or if there are specific parts of the primitives that are indented for group behaviors. It seems like the Open Connections RFC describes the current approach, and an "introduction" based approach was considered but eventually rejected?

Start with the Open Connections RFC, which the issue identifies as describing the current group approach, and compare it with the rejected “introduction” approach. Clarify how groups relate to the underlying primitives and document their security and privacy properties, including relevant compromises and concerns.