How does group moderation work?
Group level moderation allows the group creator to "boot" users from their group for whatever reason. If you started the group, it's now yours to manage. To block a user from your group, click the action menu on one of their messages in the group (not on the user's profile), and click the icon that says "Block from group." The user will get a message that they have been blocked from that particular group and will no longer be able to send or see messages. Once the user has been blocked from the group, the action can not be undone, so be sure you want to block the user in question.