Galois’s Great Theorem

  • Joseph Rotman
Part of the Universitext book series (UTX)


We prove the converse of Theorem 74: Solvability of the Galois group of f(x) ∈F[x], where F is a field of characteristic 0, implies f(x) is solvable by radicals. We begin with some lemmas; the first one has a quaint name signifying its use as a device to get around the possible absence of roots of unity in the ground field.


Galois Group Solvable Group GALOIS Theory Galois Extension Radical Extension 
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  1. 16.
    E. Houston, A Linear Algebra Approach to Cyclic Extensions in Galois Theory, Amer. Math. Monthly 100 (1993), 64–66.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Joseph Rotman
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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