must appear in the GROUP BY clause or be used in an aggregate function

Yes, this is a common aggregation problem. Before SQL3 (1999), the selected fields must appear in the GROUP BY clause[*].

To workaround this issue, you must calculate the aggregate in a sub-query and then join it with itself to get the additional columns you’d need to show:

SELECT m.cname, m.wmname, t.mx
FROM (
    SELECT cname, MAX(avg) AS mx
    FROM makerar
    GROUP BY cname
    ) t JOIN makerar m ON m.cname = t.cname AND t.mx = m.avg
;

 cname  | wmname |          mx           
--------+--------+------------------------
 canada | zoro   |     2.0000000000000000
 spain  | usopp  |     5.0000000000000000

But you may also use window functions, which looks simpler:

SELECT cname, wmname, MAX(avg) OVER (PARTITION BY cname) AS mx
FROM makerar
;

The only thing with this method is that it will show all records (window functions do not group). But it will show the correct (i.e. maxed at cname level) MAX for the country in each row, so it’s up to you:

 cname  | wmname |          mx           
--------+--------+------------------------
 canada | zoro   |     2.0000000000000000
 spain  | luffy  |     5.0000000000000000
 spain  | usopp  |     5.0000000000000000

The solution, arguably less elegant, to show the only (cname, wmname) tuples matching the max value, is:

SELECT DISTINCT /* distinct here matters, because maybe there are various tuples for the same max value */
    m.cname, m.wmname, t.avg AS mx
FROM (
    SELECT cname, wmname, avg, ROW_NUMBER() OVER (PARTITION BY avg DESC) AS rn 
    FROM makerar
) t JOIN makerar m ON m.cname = t.cname AND m.wmname = t.wmname AND t.rn = 1
;


 cname  | wmname |          mx           
--------+--------+------------------------
 canada | zoro   |     2.0000000000000000
 spain  | usopp  |     5.0000000000000000

[*]: Interestingly enough, even though the spec sort of allows to select non-grouped fields, major engines seem to not really like it. Oracle and SQLServer just don’t allow this at all. Mysql used to allow it by default, but now since 5.7 the administrator needs to enable this option (ONLY_FULL_GROUP_BY) manually in the server configuration for this feature to be supported…

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