algebraic structure

…itself—to be applied to many algebraic structures that hitherto had eluded analysis.

…the “admissible” permutations of the roots of the equation. His key discovery, brilliant and highly imaginative, was that solvability by radicals is possible if and only if the group of automorphisms (functions that take elements of a set to other elements of the set while preserving algebraic operations) is solvable,…