In MySQL:
select t1.* from test as t1
inner join
(select t2.a, min(t2.b) as min_b from test as t2 group by t2.a) as subq
on subq.a=t1.a and subq.min_b=t1.b;
Here is the proof:
mysql> create table test (id int unsigned primary key auto_increment, a int unsigned not null, b int unsigned not null, c int unsigned not null) engine=innodb;
Query OK, 0 rows affected (0.55 sec)
mysql> insert into test (a,b,c) values (1,100,90), (1,300,50), (1,200,20), (2,200,30), (2,300,70), (2,50,100);
Query OK, 6 rows affected (0.39 sec)
Records: 6 Duplicates: 0 Warnings: 0
mysql> select * from test;
+----+---+-----+-----+
| id | a | b | c |
+----+---+-----+-----+
| 1 | 1 | 100 | 90 |
| 2 | 1 | 300 | 50 |
| 3 | 1 | 200 | 20 |
| 4 | 2 | 200 | 30 |
| 5 | 2 | 300 | 70 |
| 6 | 2 | 50 | 100 |
+----+---+-----+-----+
6 rows in set (0.00 sec)
mysql> select t1.* from test as t1 inner join (select t2.a, min(t2.b) as min_b from test as t2 group by t2.a) as subq on subq.a=t1.a and subq.min_b=t1.b;
+----+---+-----+-----+
| id | a | b | c |
+----+---+-----+-----+
| 1 | 1 | 100 | 90 |
| 6 | 2 | 50 | 100 |
+----+---+-----+-----+
2 rows in set (0.00 sec)