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Galois's Theorem

An algebraic equation is algebraically solvable Iff its Group is Solvable. In order that an irreducible equation of Prime degree be solvable by radicals, it is Necessary and Sufficient that all its Roots be rational functions of two Roots.

See also Abel's Impossibility Theorem, Solvable Group

© 1996-9 Eric W. Weisstein