The minimum row on a join

I have a bit of a strange problem, please examine the following SQL

CREATE TABLE `tablea` (
    `id` INT NOT NULL AUTO_INCREMENT PRIMARY KEY ,
    `name` VARCHAR( 60 ) NOT NULL
) ENGINE = MYISAM ;

CREATE TABLE `tableb` (
    `id` INT NOT NULL AUTO_INCREMENT PRIMARY KEY ,
    `name`开发者_运维技巧 VARCHAR( 60 ) NOT NULL ,
    `refid` INT NOT NULL ,
    `position` INT NOT NULL
) ENGINE = MYISAM ;

INSERT INTO tablea (`id`,`name`) VALUE (1,'a'),(2,'b'),(3,'c');
INSERT INTO tableb (`name`, `refid`, `position`) VALUE ('a', 1, 2),('b', 1, 1);
INSERT INTO tableb (`name`, `refid`, `position`) VALUE ('a', 2, 1),('b', 2, 2);

Tableb holds 0 or more rows referencing tablea. I want to recall the records in tablea with the record in tableb that has the lowest (MIN) position. So at the moment this is a simple bit of SQL.

SELECT 
    a.id, 
    a.name AS namea,
    b.name AS nameb,
    GROUP_CONCAT(b.name),
   CAST(group_concat(b.position) AS CHAR )
FROM tablea AS a
LEFT JOIN tableb AS b
    ON b.refid=a.id
GROUP BY a.id
ORDER BY b.position ASC

If you run this you will see it output

id  namea   nameb   concat  concat
3   c   NULL    NULL    NULL
1   a   b   b,a 1,2
2   b   b   b,a 2,1

The first & second row is correct but the third I was expecting nameb to be a and not b. I have tried playing around with MIN but cannot seam to get something that always returns me what I am expecting. Any help appreciated, at the moment I am just having to do 2 queries :(

---

SELECT 
    a.id, 
    a.name AS namea,
    b.name AS nameb,
FROM tablea AS a
LEFT JOIN tableb AS b
    ON b.refid=a.id AND b.position = (SELECT min(position) FROM tableb b2 WHERE b2.rf_id = a.id)