HP OpenVMS Guide to System Security: OpenVMS Version 8.4 > Appendix A Assigning Privileges
With GROUP privilege, a user's process can control another process in the same group. The user's process is allowed to examine other processes in its own group by executing the Get Job/Process Information ($GETJPI) system service. A process with GROUP privilege can issue the SET PROCESS command for other processes in its group.
GROUP privilege is not needed for a process to exercise control over, or to examine, subprocesses that it created or other detached processes of its UIC. You should, however, grant this privilege to users who need to exercise control over the processes and operations of other members of their UIC group.