You should define who can create groups inside your domain. By default, this is set to Anyone in this domain can create groups, which allows anyone with an account in this domain to create groups:

 But you can also make it more restrictive with Only domain admins can create groups, or you can make this an open forum and enable Anyone on the Internet to create them.

Optionally, you can automatically add a suffix to the name of groups created by users; this can be anything you wish.