Using count on a join, group by required?

Greetings!

First: This is working, I just need a clarification on concept, so, it
is not necessary for you to look deeply at the SQL statement.

I have this:

Table: products that references manufacturer via
products.manufacturer_id to manufacturer.id (not important, just
informative).
Table: product_serials that references products via
product_serials.product_id to products.id

And I wanted to get this output:

Product ID, Product Name, Product Code, Manufacturer ID, Manufacturer
Name, Number of Associated Serials.

So, I build a query for that:

select products.id as product_id,products.name as name,products.code
as code,manufacturer.id as manufacturer_id,manufacturer.name as
manufacturer_name,count(product_serials.product_id) as num_serials
from products left join manufacturer on
products.manufacturer_id=manufacturer.id left join product_serials on
product_serials.product_id=products.id group by
products.id,products.name,products.code,manufacturer.id,manufacturer.name;

And it works, it gives me something like:
product_id |         name         |     code      | manufacturer_id |   manufacturer_name      | num_serials
------------+----------------------+---------------+-----------------+----------------------------+-------------
17| THE product          | 1235711131719 |              19 |
 
THE product's manufacturer |           5         6 | Car Battery 500A 12V | 7591512021575 |               8 |
Acumuladores Duncan, C.A.  |          11         1 | Test product 1       | 123456789012  |               1 |
Test Manufacturer          |           6

Which is correct, and exactly what I wanted.

So far, so good.  The thing is: the group by clause, I had to add it
because the parser forced me to, because it complained like this:

ERROR:  column "manufacturer.name" must appear in the GROUP BY clause
or be used in an aggregate function

and I had to include *all* the requested columns on the group by
clause, can anybody tell me why? or at least point to some doc that
help me understanding this?

Thanks in advance,

Ildefonso Camargo