I do not think there is a "group_proc" privilege. You are going to have to set up sudo and and specifically allow those users to become the user that runs the application. But then they can "tink" with the application process.
sudo -
man pages section 1M: System Administration Commands It is part of Solaris 11.
Suppose the app runs with appuser.
sudo su - appuser is the command they would use. I assume they are already in the same group as appuser. Let's call that group "foo"
You will have read up on
sudoedit and /
etc/sudoers You grant the permission to become "appuser" based on the fact that they are only in the special group I mentioned, "foo". Actually appuser does not have to be in the "foo" group, but then you open up access to anything that appuser can do in its own group to these newcomers.