Dozvolili su promenu.

The dictionary form is dozvoliti.

That is the infinitive, meaning the basic verb form you would look up in a dictionary.
In this sentence, dozvolili is a past-tense form built from that verb.

Su is the present-tense form of the auxiliary verb biti for they.

Serbian forms the common past tense with:

• the auxiliary biti
• plus a past participle

So here:

• su = auxiliary
• dozvolili = past participle

Together they make the past tense.

The ending -li shows that the past participle agrees with a plural masculine subject.

For example:

• dozvolio = he allowed
• dozvolila = she allowed
• dozvolili = they allowed, for a masculine or mixed-gender group
• dozvolile = they allowed, for an all-female group

So dozvolili su tells you the subject is plural and not exclusively feminine.

It is omitted, because Serbian often leaves subject pronouns out when they are understood from the verb.

So instead of saying Oni su dozvolili promenu, Serbian very naturally says just Dozvolili su promenu.

The verb form already tells you a lot about the subject.

Because su is a clitic, and clitics usually go in the second position in the sentence.

In neutral word order:

• Dozvolili su promenu.

You normally do not start the sentence with Su in standard Serbian.

Clitics like su, je, se, ga, mi often follow this second-position rule.

Because promenu is the accusative singular form of promena.

The verb dozvoliti takes a direct object, and direct objects are often in the accusative.

So:

• promena = nominative singular
• promenu = accusative singular

This is very common with feminine nouns ending in -a:

• knjiga → knjigu
• škola → školu
• promena → promenu

Because promenu is the accusative singular form of promena.

If it were plural, you would usually see:

• promene = accusative plural

So:

• Dozvolili su promenu = one change
• Dozvolili su promene = multiple changes

Yes, it matters.

Dozvoliti is perfective, so it presents the action as a completed whole: the permission was granted.

Its imperfective partner is dozvoljavati.

Compare:

• Dozvolili su promenu. = they granted/allowed the change
• Dozvoljavali su promenu. = they were allowing the change / used to allow the change

So the sentence suggests a completed act of allowing.

Yes. Serbian word order is flexible, but the focus changes.

For example:

• Dozvolili su promenu. = neutral
• Promenu su dozvolili. = puts more emphasis on the change
• Dozvolili promenu su. = unnatural in normal modern Serbian

So different word orders are possible, but not all are equally natural.

Yes. Then the participle would usually be dozvolile instead of dozvolili.

So:

• Dozvolili su promenu. = masculine or mixed group
• Dozvolile su promenu. = all-female group

This agreement is an important feature of Serbian past tense.

Yes, that is grammatically correct.

But in many situations, Serbian prefers to omit oni unless you want to:

• emphasize they
• contrast them with someone else
• make the subject especially clear

So Dozvolili su promenu often sounds more natural than Oni su dozvolili promenu in ordinary context.

It is neutral standard Serbian.

There is nothing especially formal, literary, or slangy about it.
You could hear or read this sentence in everyday speech, news, official writing, or general conversation.