In relation to group messages are the most common to use a News Forum for this.


You cant set the "Subscription mode" in the Forum to "forced subscription", 


When a person is subscribed to a Forum it means that they will be sent email copies of every subsequent post in that forum.


Your cant also use the Quickmail, if your add the Quickmail block to your course:
Turn editing on, and go down to the button. Select Quickmail in Add a block box.