Command 'groups' doesn't show group membership correctly
 

# display the groups user 'dovecot' is in
$groups dovecot
dovecot : dovecot mail
# as shown, user 'dovecot' is in group 'dovecot and group 'mail'

# display the group user 'mail' is in
$groups mail
mail : mail
# as shown, user 'mail' is in group 'mail'

# check who are the members of group 'mail' and I should see user 'dovecot' and user 'mail'
$cat /etc/group |grep mail
mail:x:8:dovecot
# however, I only see user 'dovecot' here

Is there a reason why user 'mail' is not shown as a member of group 'mail' in the last command?

Thanks!

The /etc/group file has the _secondary_ membership assignment.
The _primary_ member group assignment is in the 4th field of /etc/passwd.

if you look at /etc/passwd for the user mail, you will see its belongs to the groupid=8.

cheers