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From Proto-Indo-European*h₂r̥-sḱe-ti(“to start, rule”), which appears to be an inchoative formation from *h₂er-(“to fit, put together”), thus “to begin to fit together” > “to start, rule”. Compare Old Armenianարքայ(arkʻay, “king”), which Matzinger considered inherited from Indo-European,[1] but which is generally thought to be ultimately a borrowing from Greek.
Alternatively from a root *h₂ergʰ-(“to begin, rule, command”), perhaps cognate with Lithuanianregė́ti(“to watch, see”). (Can this(+) etymology be sourced?)