View permission / owner of full directory tree

Folder b and c are owned by user b and c. A file created by a user will belong to that user.

You can use the user permission for b and c, and the group permissions for a. If you set the SGID bit (g+s) on a folder, created files will get the group permission of that folder.

mkdir a
chown a:a a
chmod g+s a

mkdir b
chown b:a b

mkdir c
chown c:a c

(assuming all users are in a group of the same name.)

Permissions are generally not propagated by the directory that files are being copied into, rather new permissions are controlled by the user's umask. However when you copy a file from one location to another it's a bit of a special case where the user's umask is essentially ignored and the existing permissions on the file are preserved. Understanding this concept is the key to getting what you want.

So to copy a file but "drop" its current permissions you can tell cp to "not preserve" using the --no-preserve=all switch.

Example

Say I have the following file like you.

$ mkdir -m 744 somedir

$ touch afile
$ chmod 400 afile 

$ ll
total 0
-r--------. 1 saml saml 0 Feb 14 15:20 afile

And as you've confirmed if we just blindly copy it using cp we get this:

$ cp afile somedir/
$ ls -l somedir/
total 0
-r--------. 1 saml saml 0 Feb 14 15:20 afile

Now let's repeat this but this time tell cp to "drop permissions":

$ rm -f somedir/afile 

$ cp --no-preserve=all afile somedir/

$ ls -l somedir/
total 0
-rw-rw-r--. 1 saml saml 0 Feb 14 15:21 afile

So the copied file now has its permissions set to 664, where did it get those?

$ umask
0002

If I changed my umask to something else we can repeat this test a 3rd time and see the effects that umask has on the un-preserved cp:

$ umask 037
$ rm somedir/afile 

$ cp --no-preserve=all afile somedir/
$ ls -l somedir/
total 0
-rw-r-----. 1 saml saml 0 Feb 14 15:29 afile

Notice the permissions are no longer 664, but are 640? That was dictated by the umask. It was telling any commands that create a file to disable the lower 5 bits in the permissions ... these guys: (----wxrwx).