So we have shown that formula_42; however there could possibly be automorphisms there that are not in formula_32.
V sodobni abstraktni algebri je navedeno, da so enačbe druge, tretje in četrte stopnje vedno rešljive z radikali, ker so grupe simetrij formula_10 in formula_11 rešljive, grupe formula_12 pa niso rešljive za formula_13.