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Algebra Group Theory Cyclic Groups Langrange's Theorem Normal Subgroup and Quotient Group Homomorphisms Isomorphism Theorems Alternating Groups Cayley's Theorem Conjugacy Normal Subgroup of the Symmetric Groups Class Equation of Finite Group Cauchy's Theorem Sylow Theorems Simple Groups Solvable Groups Rings and Fields Ideals Quotient Rings Characteristic of a Ring Polynomial Rings Gauss Lemma Eisenstein's Irreducibility Criterion Field Extensions and Tower Low Galois Theory Algebraic Field Extensions Splitting Fields Normal Extensions Separability Finite Fields Primitive Element Theorem Galois Group of a Field Extension The Galois correspondence Ruler and Compass Constructions The Galois group of a polynomial Solvable polynomials and Galois group Quintic polynomial not solvable by radicals