Существует ли chgrp -p?

Нет. chgrpот GNU coreutils не имеет опции -p:

# chgrp --help
Usage: chgrp [OPTION]... GROUP FILE...
  or:  chgrp [OPTION]... --reference=RFILE FILE...
Change the group of each FILE to GROUP.
With --reference, change the group of each FILE to that of RFILE.

  -c, --changes          like verbose but report only when a change is made
  -f, --silent, --quiet  suppress most error messages
  -v, --verbose          output a diagnostic for every file processed
      --dereference      affect the referent of each symbolic link (this is
                         the default), rather than the symbolic link itself
  -h, --no-dereference   affect symbolic links instead of any referenced file
                         (useful only on systems that can change the
                         ownership of a symlink)
      --no-preserve-root  do not treat '/' specially (the default)
      --preserve-root    fail to operate recursively on '/'
      --reference=RFILE  use RFILE's group rather than specifying a
                         GROUP value
  -R, --recursive        operate on files and directories recursively

The following options modify how a hierarchy is traversed when the -R
option is also specified.  If more than one is specified, only the final
one takes effect.

  -H                     if a command line argument is a symbolic link
                         to a directory, traverse it
  -L                     traverse every symbolic link to a directory
                         encountered
  -P                     do not traverse any symbolic links (default)

      --help     display this help and exit
      --version  output version information and exit

Examples:
  chgrp staff /u      Change the group of /u to "staff".
  chgrp -hR staff /u  Change the group of /u and subfiles to "staff".

GNU coreutils online help: <https://www.gnu.org/software/coreutils/>
Full documentation <https://www.gnu.org/software/coreutils/chgrp>
or available locally via: info '(coreutils) chgrp invocation'

Также:

# chgrp -p 
chgrp: invalid option -- 'p'
Try 'chgrp --help' for more information.