Auto create group at registration in buddypress

Hi,

Is it possible to have a group automatically created and assigned to a user on registration with buddypress?

For example, if userA creates an account 1) either a group called userA is created or 2) perhaps we show a field where user can enter the name of the group and then it is created (similar to manually creating a group as seen here: groups/create/step/group-details/)

Hope that makes sense

Thanks

Elliot