Users Group – How to Remove a User from a Group

The usermod command will allow you to change a user's primary group, supplementary group or a number of other attributes. The -g switch controls the primary group.

For your other questions...

1. If you specify a group, groupname, that does not exist during the useradd stage, you will receive an error - useradd: unknown group groupname

2. The groupadd command creates new groups.

3. The group will remain if you remove all users contained within. You don't necessarily have to remove the empty group.

4. Create the hilbert group via groupadd hilbert. Then move David's primary group using usermod -g hilbert hilbert. (Please note that the first hilbert is the group name and the second hilbert is the username. This is important in cases, where you are moving a user to a group with a different name)

You may be complicating things a bit here, though. In many Linux distributions, a simple useradd hilbert will create the user hilbert and a group of the same name as the primary. I would add supplementary groups specified together using the -G switch.