Having your own website, gives you the power to allow who advertise there, because it is your site, your domain, you are in charge. Google groups are the owner of the group site you are using, and that is why they control who advertise there.

To get your own site, first of all, you need to register a domain name at a registrar, and then find a hosting company to host that domain for you, and then you can use various software to build and control your own site. Most good hosting companies provides you the software as well to build, manage and maintain your site.

Hope this helps!

"To get your own site, first of all, you need to register a domain name at a registrar, and then find a hosting company to host that domain for you, and then you can use various software to build and control your own site. Most good hosting companies provides you the software as well to build, manage and maintain your site."
Do you have to register a domain name??cant you just use a new name with your own extension?

Yes, you have to. Normally one register a new name when you register a domain name. You can always buy an existing one as well, but that is too expensive, it is far better and cheaper just to think of a name, then look up if it exist, if not, then register it. There are numerous domain name services available, choose the best option that suits your needs, it should not cost you more than about 10 us dollars per year to register and keep a new domain name.