Learn Turkish: Binanın ruhsatının sahte olduğunu fark ettiler. - They noticed that the building's permit is fake.

The inner sentence here is 'the permit is fake' (ruhsat sahte), which has no action verb. To turn this into a 'that' clause (the fact that it is fake), we must use the helper verb olmak combined with the -dık / -duğ- suffix.

Why is there a double genitive chain in Binanın ruhsatının?

This is a nested possessive structure. First, we form 'the building's permit' (bina-nın ruhsat-ı). Then, because this entire phrase is the subject of the -dık clause, it needs its own genitive marker (-nın) to link grammatically to the possessive ending on olduğu.

Why does olduğu end with the accusative suffix -nu?

The main verb fark etmek (to notice) takes a specific direct object. The entire clause 'that the permit is fake' is the object being noticed, so the accusative case -nu is added to olduğu to mark it as the direct object.

Why is fark ettiler written as two separate words?

Compound verbs made of a noun and a helper verb like etmek are written separately unless the noun undergoes a sound change (like a dropped vowel or doubled consonant). Because fark doesn't change its spelling, it remains a separate word from ettiler.