Restricting who can create and own Chatter groups
Key Takeaway
One permission, "Create and Own New Chatter Groups", controls both who can create new Chatter groups and who can be made the owner of new groups.
By default, any user can create Chatter groups and become their owner. Admins who want to limit this disable the "Create and Own New Chatter Groups" permission on selected user profiles.
What the permission covers
The permission is enabled by default, which is why any user can create groups until an admin disables it. It covers all three group access types: public, private, and unlisted. Its API name is ChatterOwnGroups.