write permission

Question

I'm trying to solve a problem about write permission. I have the user mamuth in the group www-data, i used the command:

adduser mamuth www-data

Running:

cat /etc/group | grep mamuth 

Results with:

adm:x:4:syslog,mamuth
cdrom:x:24:mamuth
sudo:x:27:mamuth
dip:x:30:mamuth
www-data:x:33:mamuth
plugdev:x:46:mamuth
mamuth:x:1000:
lpadmin:x:114:mamuth
sambashare:x:115:mamuth

So now when i check the /var right permission i have the following result:

drwxrwxr-x  5 www-data www-data 4096 Feb 20 15:20 www

I used the command to be sure to have right permission to write everything as mamuth (fed up to use sudo emacs to write in file):

sudo chown -R www-data:www-data /var/www/
sudo chmod -R g+w /var/www/

I don't know what's wrong while I still don't have permission as for example in /var/www/ i'm tryng to use as mamuth user the command:

emacs test

and typing some text

emacs display the message:

Buffer is read-only:  #<buffer toto>