Error: user does not exist

Hello to everyone,

I'm new to postgres-SQL. I have to admin a working solution with
postgres-SQL and cygwin unter Windows 2000.
I have cygwin dll version 1.3.17 and postgres 7.2.3-2 (output from
cygcheck -s).
From the command-line i created a new user for postgres with createuser.
I see this user in the systemtables pg_shadow and pg_user.
If i want to give that user ALL PRIVILEGES on a certain database, i get
an error:

GRANT ALL PRIVILEGES ON DATABASE bestellung TO SYSTEM;

Error: parser: parse error at or near "bestellung"

Then i tried to put that user in a certain group (that this user has
more rights, i thought):

ALTER GROUP dbadmin ADD USER SYSTEM;

Error: user "system" does not exist

I created the user SYSTEM with big characters, this is necessary in this
case.
The group dbadmin exists and is visible in pg_group.

Anyone has an idea ?
I'm new to postgres and cygwin.

Thanks a lot, and nice christmas.

Bernd