Galois Theory as Applied to the Solvability of Polynomial Equations

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Mathematics, Galois Theory, equations, algebra, solvability


Applied Mathematics | Mathematics | Physical Sciences and Mathematics


Of fundamental importance in modern algebra is the concept of a "group." There is a certain amount of freedom in the choice of defining properties; I choose properties (a), (b), and (c) below:

(a) A group G is a set of "elements" with a "rule of combination." THis rule associates with any two elements a and b of G a third element of G called the "product" of a and b (written ab) or the sum of a and b (written a+b). The rule of combination does not have to be either multiplication or addition in the "ordinary" sense.

(b) The operation is "associative"; i.e. if a, b, c are elements of G, (ab) c=a (bc).

(c) "Division" is always possible; i.e., ax=b and ya=b both have solutions in G, where a and b are arbitrary elements of G.

Department 1 Awarding Honors Status


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