Well actually what Axel suggests (i.e. custom webscript + custom UI trigger) answers exactly the need you depicted.
But I'm afraid it's too much work for someone who begins with Alfresco.
Can you please describe your exact need? We might be able to find a workaround with the default system.
For example, Alfresco have a system of "sites". Each user can create a site and is the "master" of his own site which means he can choose which users can join his site, with which rights.
So he doesn't have a total control over the groups but, depending on your needs, this might be enough and doesn't require any coding from you.