So what other database is holding the groups information for your system. Note that user inf7 is not in group A or B (which do not exist in /etc/group) and is not in group A or B in the getent group group A or B shown in the list you provided in post #3 in this thread. It is also interesting to note that there is no need to add someone to both groups; both groups have the same group ID (2560).

Note also that you have also shown us that user ad3059 does not exist in the getent group output for groups C or D either, so it appears that user ad3059 only appears in the local /etc/group file; not in the network's group database. (I say this because the grep -i a would show all occurrences of ad3059 in the network's group database.)

So, it appears that user ad3059 is not in the network's group database and only appears in the system's local files (/etc/passwd and /etc/group) where there is no group A and there is no group B.

It has been a couple of decades since I worked on a Solaris 8 system, and I don't remember how it determined who would be found in local user and group databases and who would be found in network user and group databases. I also seem to remember limits on the length's of lines in the user and group databases (both local and networked) which is probably why you have group A and B in the remote group database with the same group ID. Maybe you can't add any more users to those groups because you have reached that limit. But, I am surprised that you didn't get any error messages from usermod if that was the reason for failing to add ad3059 to those remote groups.