Abstract Algebra |
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1-1 mapping 3-cycles a₁ abelian group algebraic over F automorphism b₁ commutative ring complex numbers conjugate constructible Corollary cyclic group defined definition deg f(x degree Eisenstein Criterion element of G equivalence relation Example extension of F finite extension finite field finite group G₁ G₂ given greatest common divisor group G group of order H in G hence homomorphism homomorphism of G Homomorphism Theorem ideal of F[x induction integral domain inverse irreducible in Q[x isomorphic K₁ kernel left cosets Lemma Let F Let G maximal ideal monic polynomial multiplication N₁ nonabelian group normal subgroup number of elements permutation polynomial f(x positive integer prime number proves the theorem rational numbers reader real numbers relatively prime result of Problem S₁ Section space over F subgroup of G subset Suppose transpositions unique unit element v₁ vector space verify