Creating custom group of users & assign to user who has create DB role

Hi

I am fairly new to SQL admin stuff but am learning. I have assigned a user access to create DB using this command:

use [master]
GO
GRANT CREATE ANY DATABASE TO [user-name]
GO

So they can create and own their own DB but not muck about with any other ones, at least so I am led to believe with that statement.

Now the user is wanting to be able to add a group of users to the DB and am wondering if there 1) is a way to create a group of users and 2) assign this group/role to be accessible to this DB owner so they can add this group of users to any new DB they create?

The user can only seem to see public and guest roles/groups at the moment so obviously want them to be able to see a new group that they can select for access to the db.

Apologies if anything isn't making sense as really new to all this terminology but hope someone can work out exactly what I need to do.

Server is SQL Server 2012

Thanks

Andrew