This is the link that somehow was stripped in my previous reply:

Implementing Social Groups in DotNetNuke 6.2

Hi Ivan,
Thanks for the questions.  Please find the answers below:

Deleting a Group
- if I am a regular user (not admin) I don't have access to the security roles. So how do I delete a group I created?

We do not allow for Social Groups to be deleted by anyone other than admins at this time.  This is due to the fact that the Social Groups are the same as security roles and they have other uses throughout the site.  We do have plans to add some options so that a user can request for for a Social Group to be deleted then admins or group moderators can have the option to delete the group.

Deleting a member from a group
- when I go to the members page for a group there I can see the members (via the member directory module) but there is nothing to click to actually delete/remove an user. In the default template I have options like "add as friend", "send message" etc but not a remove from group option. Is there a token I need to include in the member directory template that does the trick?

Pretty much the same reasoning as the first question, but we do plan to add options so that group owners can manage members more easily.

 Inviting a member to a private group
- I see the option to make the group private and it works. How do I invite group members to a private group though. Again I am not an admin so I can't just add them to the security role.

Private group membership is intended to be managed by admins or through the API.  We do have plans to add a feature so that other users can invite members to public groups. 

Thanks for the feedback!