diff --git a/core/pyos.py b/core/pyos.py
index 215effb3cb..2454dabe56 100644
--- a/core/pyos.py
+++ b/core/pyos.py
@@ -308,8 +308,8 @@ def InitShell(self):
     """Always called when initializing the shell process."""
     pass
 
-  def InitInteractiveShell(self, display):
-    # type: (_IDisplay) -> None
+  def InitInteractiveShell(self, display, my_pid):
+    # type: (_IDisplay, int) -> None
     """Called when initializing an interactive shell."""
     # The shell itself should ignore Ctrl-\.
     signal.signal(signal.SIGQUIT, signal.SIG_IGN)
@@ -331,6 +331,16 @@ def InitInteractiveShell(self, display):
     self.sigwinch_handler = SigwinchHandler(display, self)
     signal.signal(signal.SIGWINCH, self.sigwinch_handler)
 
+    try:
+      # Put the interactive shell in its own process group, named by its PID
+      posix.setpgid(my_pid, my_pid)
+      # Attach the terminal (stdin) to the progress group
+      posix.tcsetpgrp(0, my_pid)
+
+    except (IOError, OSError) as e:
+      # For some reason setpgid() fails with Operation Not Permitted (EPERM) under pexpect?
+      pass
+
   def AddUserTrap(self, sig_num, handler):
     # type: (int, Any) -> None
     """For user-defined handlers registered with the 'trap' builtin."""
diff --git a/core/shell.py b/core/shell.py
index 301133c5df..7a57d5ad5e 100644
--- a/core/shell.py
+++ b/core/shell.py
@@ -630,7 +630,7 @@ def Main(lang, arg_r, environ, login_shell, loader, line_input):
     else:  # Without readline module
       display = comp_ui.MinimalDisplay(comp_ui_state, prompt_state, debug_f)
 
-    sig_state.InitInteractiveShell(display)
+    sig_state.InitInteractiveShell(display, my_pid)
 
     # NOTE: called AFTER _InitDefaultCompletions.
     with state.ctx_ThisDir(mem, rc_path):
diff --git a/spec/stateful/harness.py b/spec/stateful/harness.py
index 3b90c0beab..f6cad25b73 100644
--- a/spec/stateful/harness.py
+++ b/spec/stateful/harness.py
@@ -38,12 +38,14 @@ def send_signal(name, sig_num):
   os.kill(get_pid_by_name(name), sig_num)
 
 
-# XXX: osh.sendcontrol("z") does not suspend the foreground process :(
-#
-# why does osh.sendcontrol("c") generate SIGINT, while osh.sendcontrol("z")
-# appears to do nothing?
 def stop_process__hack(name):
-  """Send sigstop to the most recent process matching `name`"""
+  """Send sigstop to the most recent process matching `name`
+
+  Hack in place of sh.sendcontrol('z'), which sends SIGTSTP.  Why doesn't OSH
+  respond to this, or why don't the child processes respond?
+
+  TODO: Fix OSH and get rid of this hack.
+  """
   send_signal(name, signal.SIGSTOP)
 
 
diff --git a/test/group-session.sh b/test/group-session.sh
index 6cc6951614..335869727e 100755
--- a/test/group-session.sh
+++ b/test/group-session.sh
@@ -3,15 +3,63 @@
 # Test kernel state: the process group and session leader.
 #
 # Usage:
-#   ./group-session.sh <function name>
+#   test/group-session.sh <function name>
 
-set -o nounset
-set -o pipefail
-set -o errexit
+setup() {
+  mkdir -p _tmp
+  ln -s -f -v $(which cat) _tmp/cat2
+}
+
+show_group_session() {
+  # by default, it shows processes that use the same terminal
+  #ps -o pid,ppid,pgid,sid,tname,comm | cat | _tmp/cat2
+
+  # - bash is the parent of ps, cat, ca2
+  # - the PGID is the same as bash?  Oh this is for a NON-INTERACTIVE SHELL.
+  # - TPGID: controlling terminal's notion of foreground pgid?
+  #   - it's always the same number, so it's misleading to associate with a process
+  #   - see APUE section on setpgid(), tcsetgprp()
+
+  if true; then
+    echo '[foreground pipeline]'
+    ps -o pid,ppid,pgid,sid,tpgid,comm | cat | _tmp/cat2
+  fi
+
+  # Test background pipeline
+  if false; then
+    # For interactive shells, the TPGID is different here.
+    # Foreground: it matches the PGID of 'ps | cat | cat2'
+    # Background: it matches the PGID of bash!
+
+    echo '[background pipeline]'
+    ps -o pid,ppid,pgid,sid,tpgid,comm | cat | _tmp/cat2 &
+    wait
+  fi
+
+  # Test plain process
+  if false; then
+    echo '[single process]'
+    ps -o pid,ppid,pgid,sid,comm
+  fi
+}
+
+compare_shells() {
+  for sh in dash bash mksh zsh bin/osh; do
+  #for sh in dash bash; do
+    echo -----
+    echo $sh
+    echo -----
+
+    echo 'NON-INTERACTIVE'
+    $sh $0 show_group_session
+    echo
 
-show() {
-  # by deafult, it shows processes that use the same terminal
-  ps -o pid,ppid,pgid,sid,tname,comm
+    echo INTERACTIVE
+    $sh -i -c '. $0; show_group_session' $0
+    echo
+  done
 }
 
-"$@"
+if test $(basename $0) = 'group-session.sh'; then
+  "$@"
+fi