Synonyms for Turkmen (same or very similar meaning)
WordNet sense 1 (a member of a Turkic people living in Turkmenistan and neighboring areas):
Turcoman, Turkoman
WordNet sense 2 (a republic in Asia east of the Caspian Sea and south of Kazakhstan and north of Iran; an Asian soviet from 1925 to 1991):
Turkmenia, Turkmenistan, Turkomen
From the ODE community, based on WordNet
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