Abstract
This chapter discusses equations solvable by radicals. A normal extension K of the field P is called a cyclic extension if its Galois group G(K, P) is cyclic. As an example of a cyclic extension, one can take a simple radical extension defined by a binomial equation of degree n, with the condition that the fundamental field P contains a primitive nth root of unity. If the field P contains a primitive nth root of unity, then any cyclic extension K of it of degree n is a simple radical extension, which is defined by an irreducible binomial equation of degree n. The Galois group of any normal subfield of an arbitrary normal radical extension is a solvable group. The converse is also true: any normal field, having a solvable Galois group, is a subfield of some normal radical extension. The normal fields with solvable Galois group are exhausted by the normal subfields of normal radical extensions.
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