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Linear Groups with an Exposition of Galois Field Theory

Leonard Eugene Dickson
Publisher: 
Dover Publications
Publication Date: 
2003
Number of Pages: 
312
Format: 
Hardcover
Series: 
Dover Phoenix Editions
Price: 
52.50
ISBN: 
0-486-49548-5
Category: 
Monograph
We do not plan to review this book.
I.
Introduction to the Galois Field Theory
1. Definition and properties of finite fields
2. Proof of the existence of the GF[pm] for every prime p and integer m
3. Classification and determination of irreducible quantics
4. Miscellaneous properties of Galois Fields
5. Analytic representation of substitutions on the marks of a Galois Field
II. Theory of Linear Groups in a Galois Field
1. General linear homogeneous group
2. The Abelian linear group
3. A generalization of the Abelian linear group
4. The hyperabelian group
5. The hyperorthogonal and related linear groups
6. The compounds of a linear homogeneous group
7. Linear homogeneous group in the GF[pn], p>2, defined by a quadratic invariant
8. Linear homogenous group in the GF[2n], defined by a quadratic invariant
9. Linear groups with certain invariants of degree q>2
10. Canonical form and classification of linear substitutions
11. Operators and cyclic subgroups of the simple group LF(3, pn)
12. Subgroups of the linear fractional group LF (2, pn)
13. Auxiliary theorems on abstract groups. Abstract forms of various linear groups
14. Group of the equation for the 27 straight lines on a general surface of the third order
15. Summary of the known systems of simple groups
Index

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