(coreutils.info)Directory Setuid and Setgid

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27.5 Directories and the Set-User-ID and Set-Group-ID Bits
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On most systems, if a directory’s set-group-ID bit is set, newly created
subfiles inherit the same group as the directory, and newly created
subdirectories inherit the set-group-ID bit of the parent directory.  On
a few systems, a directory’s set-user-ID bit has a similar effect on the
ownership of new subfiles and the set-user-ID bits of new
subdirectories.  These mechanisms let users share files more easily, by
lessening the need to use ‘chmod’ or ‘chown’ to share new files.

   These convenience mechanisms rely on the set-user-ID and set-group-ID
bits of directories.  If commands like ‘chmod’ and ‘mkdir’ routinely
cleared these bits on directories, the mechanisms would be less
convenient and it would be harder to share files.  Therefore, a command
like ‘chmod’ does not affect the set-user-ID or set-group-ID bits of a
directory unless the user specifically mentions them in a symbolic mode,
or uses an operator numeric mode such as ‘=755’, or sets them in a
numeric mode, or clears them in a numeric mode that has five or more
octal digits.  For example, on systems that support set-group-ID
inheritance:

     # These commands leave the set-user-ID and
     # set-group-ID bits of the subdirectories alone,
     # so that they retain their default values.
     mkdir A B C
     chmod 755 A
     chmod 0755 B
     chmod u=rwx,go=rx C
     mkdir -m 755 D
     mkdir -m 0755 E
     mkdir -m u=rwx,go=rx F

   If you want to try to set these bits, you must mention them
explicitly in the symbolic or numeric modes, e.g.:

     # These commands try to set the set-user-ID
     # and set-group-ID bits of the subdirectories.
     mkdir G
     chmod 6755 G
     chmod +6000 G
     chmod u=rwx,go=rx,a+s G
     mkdir -m 6755 H
     mkdir -m +6000 I
     mkdir -m u=rwx,go=rx,a+s J

   If you want to try to clear these bits, you must mention them
explicitly in a symbolic mode, or use an operator numeric mode, or
specify a numeric mode with five or more octal digits, e.g.:

     # These commands try to clear the set-user-ID
     # and set-group-ID bits of the directory D.
     chmod a-s D
     chmod -6000 D
     chmod =755 D
     chmod 00755 D

   This behavior is a GNU extension.  Portable scripts should not rely
on requests to set or clear these bits on directories, as POSIX allows
implementations to ignore these requests.  The GNU behavior with numeric
modes of four or fewer digits is intended for scripts portable to
systems that preserve these bits; the behavior with numeric modes of
five or more digits is for scripts portable to systems that do not
preserve the bits.