pg, mysql comparison with "group by" clause

I'm not sure what I was thinking, but I tried the following query in pg:

SELECT * FROM t GROUP BY state;

pg returns an error.

Mysql, OTOH, returns the first row for each state.  (The first row with
"AK", the first row with "PA", etc.)  

I'm no SQL expert, but it seems to me that the pg behavior is correct, and
the mysql result is just weird.  Am I correct?