Final answer:
The command to change a file's group owner is 'chgrp'. It is executed by specifying the group name and the file name, and requires the appropriate permissions or superuser privileges.
Step-by-step explanation:
The command that changes a file's group owner in Linux and Unix systems is chgrp. To use this command, you would typically enter chgrp followed by the group name you want to assign to the file, and then the file name. For example, if you want to change the group ownership of a file named example.txt to a group called editors, you would use the command chgrp editors example.txt. It is important to have the necessary permissions or to execute this command with superuser privileges for it to be effective.