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Just like their also arawak Eigner (E-i-gen-ne-er) relatives Gemeiners may also come from igneri tribe and the doric city of Erineos related to dórs in Myndos now called in arawak regions duri-mundu.
It may have had inhabitants from magnét tribe which explains this name so : Gen-ma-I-ne-er.
Possibly there was a tribe called mag'n-it-ineeri as well, as spelling and pronounciation of already "extinct" names varies at different authors.
See Garfunkel,Fogarasi,Eigner and Inotay !
Balázs Déri's idea