Ko te kaupapa taketake mo te kaupapa rōpū ko te rapu mo nga rongoā o nga whārite polynomial o te tohu teitei ake i te 4. I timata te 19th-rau French mathematician Évariste Galois (1888) ki te whakawhānui i te mahi o mua o Paolo Ruffini me Hohepa-Louis Lagrange, i hoatu he paearu mo te solvability o te whārite polynomial motuhake i roto i ngā o te rōpū symmetry o ona pakiaka (ngā rongoā). Ko nga huānga o taua rōpū Galois ōrite ki etahi permutations o nga pakiaka. I te tuatahi, i whakakahoretia whakaaro o Galois e ona hoa, ka whakaputaina anake posthumously. I tirotirohia i roto i ngā ngā rōpū whānui e Louis C. Cayley o runga i te ariā o ngā rōpū, i runga i te whārite axial teitei ake i te 4. I te rau tau 1870-1888, ka hoatu e te 19th-rau French mathematician Évariste Galois, whakawhānui i te mahi o mua o Paolo Ruffini me Hohepa-Louis Lag
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