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This classic in the field of abstract algebra has been called "the first systematic treatment of finite fields in the mathematical literature." Divided into two sections-"Introduction to the Galois Field Theory" and "Theory of Linear Groups in a Galois Field"-and crammed with examples and theorems, Linear Groups remains relevant more than a century after its publication. Learn about: . definition and properties of finite fields . classification and determination of irreducible quantics . miscellaneous properties of Galois Fields . analytic representation of substitutions on the marks of a Galois Field . the Abelian linear group . the hyperabelian group . the hyperorthogonal and related linear groups . and much more. This historic contribution to the theory of groups is still appreciated by mathematicians today. American mathematician LEONARD EUGENE DICKSON (1874-1954) received the University of Chicago's first doctorate in mathematics, and later taught there for 39 years. His published works include Linear Algebras (1914), History of the Theory of Numbers (1919-23), and Studies in the Theory of Numbers (1930).