The setgid permission is similar to the setuid permission. The process's effective group ID (GID) is changed to the group that owns the file, and a user is granted access based on the permissions that are granted to that group. The /usr/bin/mail command has setgid permissions:
-r-x--s--x 1 root mail 67504 Jun 17 12:01 /usr/bin/mail
When the setgid permission is applied to a directory, files that were created in this directory belong to the group to which the directory belongs. The files do not belong to the group to which the creating process belongs. Any user who has write and execute permissions in the directory can create a file there. However, the file belongs to the group that owns the directory, not to the group that the user belongs to.
You should monitor your system for any unauthorized use of the setgid permission to gain superuser capabilities. A suspicious permission grants group access to such a program to an unusual group rather than to root or bin. To search for and list all files that use this permission, see How to Find Files With Special File Permissions.