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In a Global Form for  UCSD  Department of Mathematics  Math Ucsd

In a Global Form for UCSD Department of Mathematics Math Ucsd

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hello in the previous lecture we proved um galway's solvability theorem at least once one direction what is the statement it says that if f is a field of a characteristic zero and small f is a polynomial with coefficients inside the field capital f suppose k is a splitting field of this binomial over the base field capital f then if the polynomial small f is solvable by radicals over the base field capital f and this should this should be emphasized so if it is solvable by radicals over the base field capital f then the group of f automorphisms of the splitting field k is a solvable group and let's recall that a group is called solvable if it has a chain of subgroups such that the factors of each one by the next one is an abelian group now today we are going to use this theorem and show that there are some polynomials um that are there are there are some polynomials with coefficients inside q that are not solvable by radicals there are some binomials of degree five that

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