Learn French: Beaucoup de gens utilisent l'anonymat pour dénigrer autrui publiquement. - A lot of people use anonymity to publicly denigrate others.

Autrui is an invariable pronoun meaning "other people" in a broad, general sense. It's more formal and abstract than les autres (the others), making it perfect for sweeping statements about society, ethics, or human behavior like this one.

I usually see autrui after a preposition. Is it normal to use it as a direct object here in dénigrer autrui?

Yes! While autrui is most frequently used after prepositions (like le respect d'autrui or penser à autrui), it can absolutely function as a direct object, as it does here. Keep in mind, however, that autrui can never be the subject of a sentence.

As a refresher, why is it beaucoup de gens and not beaucoup des gens?

Adverbs of quantity like beaucoup, trop, and assez are followed by a simple de (or d') when talking about things in general. You would only use des (which is a contraction of de + les) if you were talking about a specific, defined group, like "a lot of the people in this room."

Could the adverb publiquement go immediately after dénigrer instead of at the end of the sentence?

Yes, pour dénigrer publiquement autrui is grammatically correct, as adverbs normally follow the infinitive verb they modify. However, placing the adverb at the very end of the phrase is a common stylistic choice that puts extra emphasis on the public nature of the act.