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I assume you've seen
Registration Codes. I actually want to use that, but there's a file that the dev needs to update to make it work with XOOPS 2.0.10+ and it hasn't happened yet. (hint)
I recall seeing a forum post here about a groups module but there was some contention over it with the moderators and it the thread was deleted. It's gone from my notifications list too, so I can't point you to it.
A user-created groups feature is a pretty rare beast. In the past, I've looked at 'Siteframe Lagrange' (superceded by
Siteframe Beaumont Beta 4) and Alstrasoft's '
eFriends' (a commercial clone of Tribe.net). Both let users create groups. Siteframe was o.k. but the dev was serious about the non-commercial Creative Commons licence. Haven't tried the new release.
eFriends is an excellent concept but visually messy. They keep adding new features without resolving existing issues.
I have some notes on a couple of other commercial solutions somewhere if you're interested.
A thread is for life. Not just for Christmas.