On the group pages there is no "Join Group Button" I think this should be something to consider adding for a future release. This is already available for Events which makes less sense to me than it does groups.

See here (Group Main Page): http://screencast.com/t/K2p8l7kve
See here (Event Main Page): http://screencast.com/t/h8h1pcVWTp

Something to consider adding.

Thanks,
James