They got married
the same as
They have got married
Is word "have" is ommited from the first sentence? But both have the same meaning. If not, why is got used with an adjective "married"?
married is not an adjective but a past participle. Your verb is
to get married.
The difference between the sentences is that the verb is at different tenses. First is at past tense simple, the second one is at present perfect simple.
Past tense simple is used to describe past actions where the time has been specified.
They got married yesterday. They got married last year.
Present perfect simple is used to describe past actions where the time has not been specified.
They have got married. but we don't know when