Hello.

Could you please go to properties of Group registration web part and uncheck "Require approval" property? If checked, the group will have to be approved by a site administrator before it is published on the site, so you need to uncheck it. You can find more info here: http://devnet.kentico.com/docs/devguide/enabling_users_to_create_groups.htm

Best Regards,
Radek Macalik