"Abelian groups were named after Norwegian mathematician Niels Henrik Abel by Camille Jordan because Abel found that the commutativity of the group of a polynomial implies that the roots of the polynomial can be calculated by using radicals"
"Historically, the word solvable arose from Galois theory and the proof of the general unsolvability of quintic equation."
Question. Where do nilpotent groups come from ? Who defined them first ? For what purpose ? Any reference ?