[Typo3] OpenLDAP group membership problems

[Pieter]

My setup:
Typo3 3.7 with ldap_lib, ldap_server, ldap_sync, ldap_auth, cc_sv_auth
phpBB 2.0.11 with ldap Auth mod 1.1.8
Debian Linux with slapd 2.1.30-3 (OpenLDAP server)

I have LDAP partially working in phpBB and in Typo3.  "Group membership" 
is a problem in both cases. 
It seems as if both phpBB and Typo3 expect (within the record of a 
person) an attribute that contains the groups the person belongs too.  
Example of this structure: the user "Pieter" is member of the groups 
"admin" and "contest"

In contrast with this, my OpenLDAP database only allows a separate group 
record (with the objectClass "groupOfNames") in the database that holds 
a list of persons that belong to the group.
Example of this structure: the group "contest" contains the users 
"Pieter", "Ellen" and "Bob"

The first way is how it's done in Active Directory.   
I'm lost in LDAP-space. Can anyone point me to good (Open)LADP sources 
on the web? Is there an example available of the OpenLDAP structures 
needed to do group management the Active Directory way?

The problem might have something to do with the schema's used by the 
slapd OpenLDAP server. These schema's are:
core.schema
cosine.schema
nis.schema
inetorgperson.schema
 
Cheers
Pieter