Politiet undersøker mafiaen.

In Norwegian, the definite article is usually attached to the end of the noun instead of appearing as a separate word before it.

• politi = police
• politiet = the police

and

• mafia = mafia
• mafiaen = the mafia

So Politiet undersøker mafiaen literally looks like Police-the investigates mafia-the, but in natural English it is The police are investigating the mafia.

Because politi is a neuter noun in Norwegian, and neuter nouns normally take -et in the definite singular.

• et politi = a police force / a police authority
• politiet = the police

By contrast, many common-gender nouns take -en:

• en bil → bilen
• en mafia → mafiaen

So the different endings reflect grammatical gender, not meaning.

Grammatically, politiet is singular in Norwegian, even though in English the police is treated as plural.

That is why Norwegian uses one noun form, politiet, with no plural marking here. Norwegian present-tense verbs also do not change depending on whether the subject is singular or plural, so you cannot see number from the verb anyway.

A useful way to think about it is:

• Norwegian: politiet = one collective institution
• English: the police = a plural-looking expression

So the grammar does not match English exactly, even though the meaning does.

Undersøker is the present tense of the verb å undersøke, which means to investigate, to examine, or to look into, depending on context.

• å undersøke = to investigate
• undersøker = investigates / is investigating

In this sentence, English would most naturally say are investigating, but Norwegian often uses the simple present where English prefers the present progressive.

So:

• Politiet undersøker mafiaen
  = The police are investigating the mafia

Because Norwegian verbs do not agree with the subject in person or number in the present tense.

Compare:

• Jeg undersøker = I investigate / am investigating
• Du undersøker = you investigate / are investigating
• Politiet undersøker = the police investigate / are investigating

The verb form stays undersøker in all of these.

This is much simpler than English, where you have forms like I investigate but he investigates.

This is the normal Norwegian subject–verb–object order in a main clause:

• Politiet = subject
• undersøker = verb
• mafiaen = object

So it follows the same basic pattern as English:

• The police
  • are investigating
    • the mafia

If you changed the sentence into a question or moved another element to the front, Norwegian would often use its verb-second pattern, but in this plain statement the order is straightforward.

Because the sentence refers to the mafia, not just mafia in a general sense.

• mafia = mafia, mafia as a concept, or an indefinite use in some contexts
• mafiaen = the mafia, a specific criminal organization or the mafia as a known group

Norwegian usually marks definiteness directly on the noun, so if English has the mafia, Norwegian normally has mafiaen.

Yes, å undersøke is a flexible verb. It can mean things like:

• investigate
• examine
• inspect
• look into

The exact translation depends on context.

In Politiet undersøker mafiaen, the most natural meaning is investigate or look into, because the subject is the police and the object is the mafia. So this is clearly about a police investigation, not a physical examination.

A rough English-friendly guide is:

• Politiet ≈ poo-lee-TEE-uh
• undersøker ≈ UN-der-suh-kur
• mafiaen ≈ ma-FEE-ah-en

A few helpful notes:

• The r in Norwegian is usually pronounced more clearly than in many English accents.
• The letter ø in undersøker does not exist in English. It is somewhat like the vowel in French peu or German schön.
• In normal speech, some syllables may sound a bit shorter or more reduced than in careful pronunciation.

Exact pronunciation varies by dialect, but this gives you a good starting point.

Yes. Etterforsker is often even more specifically connected to criminal investigation.

Compare:

• undersøker = investigates, examines, looks into
• etterforsker = investigates in a police/criminal sense

So:

• Politiet undersøker mafiaen = The police are investigating / looking into the mafia
• Politiet etterforsker mafiaen = The police are investigating the mafia

Both can work, but etterforsker sounds more explicitly like a formal criminal investigation.

Not in this sentence.

When a noun is in the definite form, you normally do not add en or et before it unless there is also an adjective structure that requires double definiteness.

So here:

• politiet already means the police
• mafiaen already means the mafia

You would not say:

• en mafiaen
• et politiet

Those are incorrect.

If the nouns were indefinite, then you would use the indefinite article where appropriate:

• et politi = a police authority / a police body
• en mafia = a mafia / a mafia group (less common depending on context)

But in the sentence given, both nouns are definite.