MySQL combining multiple columns with GROUP_CONCAT, per row

I have some objects which have duplicates. One table stores the objects (the 'primaries'); another stores the one-to-many relation of objects to their duplicates (the 'secondaries'):

Objects
-------
`obj`
A1
A1a
A1b
A2

Duplicates
----------
`primary`,`secondary`
A1, A1a
A1, A1b

I'm trying to devise a single query that uses GROUP_CONCAT to return a summary of objects and their duplicates, returning one row per object: [obj, primary, combined secondary columns], like:

 A1,   A1,(A1a,A1b)
 A1a,  A1,(A1a,A1b)
 A1b,  A1,(A1a,A1b)
 A2,   NULL

Trying to do

SELECT `obj`, `primary`, GROUP_CONCAT(`secondary`) 
FROM `Objects`
LEFT JOIN `Duplicates` on (`obj`=`primary` OR `obj`=`secondary`)

is returning only a single row, containing a concat of all secondaries from all rows:

 a1a,a1a,  a1b,a1b,a1c,a1c,a2b,a2b

Thanks for any help!

@PM 77-1 (thanks) suggested adding a GROUP BY clause. I tried this:

SELECT `obj`, `primary`, GROUP_CONCAT(`secondary`) 
FROM `Objects`
LEFT JOIN `Duplicates` on (`obj`=`primary` OR `obj`=`secondary`) GROUP BY `obj`

which improved things, and gives 4 rows, one for each instance of obj, and the results are what I want for A1 and A2, but each of obj A1a and A1b should be A1a,A1b.

obj primary GROUP_CONCAT(`secondary`)
A1  A1      A1a,A1b
A1a A1      A1a
A1b A1      A1b
A2  NULL    NULL

[BTW I forgot that primary is a reserved word so in my test implementation this is actually primaryy!]

So, still stuck on this...

Edit:

I'm not stuck anymore! The result above is what I wanted! Thanks to @PM 77-1.