ELEMENTS
id, name 
1   элем1
2   элем2
3   элем3


ELEMENT_USER_GROUP
element_id, user_id
1           3
1           4
2           4


ELEMENT_STRINGS
id,  element_id, user_id
1    1           3   
2    1           4
3    1           7
4    2           5
5    2           8

У меня должны выйти:
element_id   ELEMENT_STRINGS.id  user_id
1             1                   3
2             4                   5

SELECT
`e_u_g`.`element_id`,
MIN(`e_s`.`id`),
`e_s`.`user_id` AS `user_id_all`

FROM  `ELEMENT_USER_GROUP` AS `e_u_g`
LEFT JOIN `ELEMENT_STRINGS` AS `e_s` ON `e_s`.`element_id` = `e_u_g`.`element_id`

WHERE `e_u_g`.`user_id` = '2'
GROUP BY `e_s`.`element_id`

#1055 - Expression #3 of SELECT list is not in GROUP BY clause and contains nonaggregated column 'e_s.user_id' which is not functionally dependent on columns in GROUP BY clause; this is incompatible with sql_mode=only_full_group_by