Careful here — the line above describes the country, but the country is Turkmenistan, and the word Turkmen means something a bit narrower. Turkmen is the people, the language, and the adjective. A Turkmen is a person of that ethnic group, most of whom live in Turkmenistan, though there are also large numbers in Iran and Afghanistan. Turkmen is also the language they speak, which is a Turkic language, related to Turkish but not the same — a Turkish speaker and a Turkmen speaker can catch some of each other's words, the way a Mandarin speaker catches some Cantonese, but they are not simply the same language. And Turkmen works as an adjective: Turkmen carpets, Turkmen music, the Turkmen language. The plural is usually Turkmen too, unchanged, like sheep — "three Turkmen", not "three Turkmens", although you will see Turkmens written sometimes and nobody will misunderstand you. The older English word for the same people is Turkoman or Turcoman, which you meet in history books and carpet catalogues. This is a low-frequency word. You will meet it in news reports, in geography class, and on the label of an expensive rug, and almost nowhere else. Do not worry about producing it; recognising it is enough.