A simple but nasty query ... (group by line order)

[Pedro Ribeiro]

I'm developing an application that uses MySQL, at this time I’m having trouble doing a query (involving multiple tables, etc) that I can resume to this simple problem:

One table with 3 columns named "a","b","c" with values (in this order):

mysql> select * from test;
+---+---+---+
| a | b | c |
+---+---+---+
| 1 | 2 | 2 |
| 1 | 3 | 1 |
| 2 | 2 | 2 |
+---+---+---+

I want a query to return-me one line for each "a" existing, that line should be the one with the bigger value of "b". In this case:

+---+---+---+
| a | b | c |
+---+---+---+
| 1 | 3 | 1 |
| 2 | 2 | 2 |
+---+---+---+

It seems simple no?
The problem is that sorting (in GROUP BY or ORDER BY) seems to apply only after grouping and the result I’m having is:
+---+---+---+
| a | b | c |
+---+---+---+
| 1 | 2 | 2 |
| 2 | 2 | 2 |
+---+---+---+

Any suggestion to a query that does it right?
How do I select witch line represents the group when using GROUP BY?
Thanks!