Where does “Hadesarchaea” come from?

Hadesarchaea (Translingual) comes from Ancient Greek ἀρχαῖα, from Ancient Greek ἀρχαῖος, from Ancient Greek ἀρχή, from Ancient Greek ἄρχω, from Proto-Indo-European h₂ergʰ- — to begin; to command, rule; to begin, rule,...

Ancestry of “Hadesarchaea”, step by step

Step	Language	Word	Meaning
1	Ancient Greek	ἀρχαῖα	neuter nominative/accusative/vocative plural of...
2	Ancient Greek	ἀρχαῖος	Pertaining to the beginning; ancient, primeval
3	Ancient Greek	ἀρχή	beginning, origin; sovereignty, dominion,...
4	Ancient Greek	ἄρχω	To begin; To lead, rule, govern, command; To be...
5	Proto-Indo-European	h₂ergʰ-	to begin; to command, rule; to begin, rule,...

Every word from Proto-Indo-European h₂ergʰ- →