From Wikipedia:

"**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"

From Wikipedia's article on solvable groups:

"Historically, the word **solvable** arose from Galois theory and the proof of the general unsolvability of quintic equation."

Question.Where donilpotent groupscome from ? Who defined them first ? For what purpose ? Any reference ?

résolubleand has two English translations in use: the most commonsolvableand alsosoluble$\endgroup$4more comments