Fog Bugs User Groups are described in their help articles, but the FogBugz API Documentation does not mention a method for interacting with them.
How can I add and remove users from a FogBugz UserGroup programmatically?
From FogBugz Support:
There currently isn’t any support for modifying User Group membership using either our published XML API or our unpublished (in progress) JSON API. We do have an outstanding issue to add access to User Groups via the API, and I’ll add your vote to that case.