http://www.newtolinux.org.uk/tutoria...missions.shtml
there is difference between root(owner) and group(what you are using)
a file would be like this
rwxr--r-- (ie 744 would be readable and and writable only by root, and not the group,which has only read permission).
If you want to make mozilla available to other users you could also try suid
(see manpage of chmod
man chmod
and
man chgrp
and
man chown
)