#### Title

Galois Theory as Applied to the Solvability of Polynomial Equations

#### Publication Year

1957

#### Keywords

Mathematics, Galois Theory, equations, algebra, solvability

#### Disciplines

Applied Mathematics | Mathematics | Physical Sciences and Mathematics

#### Abstract

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

Mathematics

#### Recommended Citation

Young, L.
(1957).
*Galois Theory as Applied to the Solvability of Polynomial Equations* (Undergraduate honors thesis, University of Redlands).
Retrieved from https://inspire.redlands.edu/cas_honors/259