To answer my own question,
an elusive line in the documentation for creating documents (http://
apidocs.mendeley.com/home/user-specific-methods/user-library-create-
document) states:
This document is a JSON object which can include the following fields:
'title', 'type', 'authors', 'volume', 'issue', 'url', 'doi', 'pmid',
'tags', 'notes', 'keywords', 'pages', 'year', 'publisher', 'abstract',
'isbn', 'issn', 'country', 'genre'.
--------> In order to create a group document (either in a private,
invite-only or public group), group_id must be added to the object.