If user A is member of group foo, is it then possible for A to share a file for all members within foo without root permissions?
chown foo:foo file
Is not permitted without privileges.
A can say
chmod o+rw file
but if A do not want to make it public for other users than those within foo, that does not work.
chown foo:foo file
Is not permitted without privileges. -> It's also not permitted with privileges iffoo
is not a group. If you want to share by changing just the group, just change the group:chown :foo file
(does not require privileges).