A Book of Abstract Algebra

a₁ a₁x abelian group automorphism b₁ bijective function c₁ called Chapter closed with respect coefficients congruences constructible contains coset cycle of length cyclic group denote element of G element of order equal equations equivalence relation example Exercise extension of F factor finite extension fixes F fixfield function f Gal(K Galois group group G group of order hence HINT homomorphic image ideal injective integer integral domain inverse irreducible polynomial isomorphism K₁ Let F Let G Let H mathematics minimum polynomial nonzero normal subgroup nth roots number of elements operation ord(a polynomial a(x positive integer prime number properties Prove that G Prove the following quotient group real numbers relatively prime ring with unity root field root of unity roots of a(x solvable group subgroup of G subring subset Suppose surjective Theorem transpositions