+-----------+----------+-------+
| member_id | group_id | score |
+-----------+----------+-------+
|         1 |        1 |    12 |
|         2 |        1 |     2 |
|         3 |        1 |    20 |
|         4 |        2 |    40 |
|         5 |        2 |     4 |
|         6 |        3 |    19 |
|         7 |        3 |    17 |
+-----------+----------+-------+

SELECT MAX(IF(score = MAX(score), member_id, NULL)) AS member
FROM members
GROUP BY group_id

+-----------+
| member_id |
+-----------+
|         3 |
|         4 |
|         6 |
+-----------+