Yes, it's possible. It's even easy.
SELECT email, GROUP_CONCAT(DISTINCT group_name ORDER BY g.group_id) AS groups
FROM Users AS u
JOIN users_groups AS ug ON u.user_id = ug.user_id
JOIN Groups AS g on ug.group_id = g.group_id
GROUP BY email
ORDER BY email
That will display one line per email, with the distinct groups belonging to that user shown in order of group id. T