You should be able to use GlideUser API in the condition for the UI action and check if the current user is a member of the group, example:
gs.getUser().isMemberOf('Assignment Group')
You can detailed info about using '.isMemberOF' here: https://developer.servicenow.com/dev.do#!/reference/api/utah/server_legacy/GUserAPI#GUser-isMemberOf...
