So long as a group is open, and doesn't require approval to join, it should be possible for any member to invite people to the group.  This should not be reserved to the administraters of the group.

People don't want to get spammed invites. Administrators are often responsible enough to send out invites in moderation, and regular members are not.

Administrators, regular members, they're all just people on the website.  I don't think creating a group makes you a responsible member and joining the group later makes you inherently more likely to be abusive.  That's silly.  Plus, if you have to type the names of the members you're inviting, then mass invite spams are not a risk.  I just want to be able to invite my friends on the site to the group I joined because I think they'd be interested, and it's a more direct way than telling them each individually about it.

One method of achieving this is to create your own group B, then use the Invite Members dialog from there to invite people to your first group A.