MA5301: Finite Groups and Finite Fields
Text
I. Martin Isaacs , Algebra A Graduate Course, Brooks \&
Cole, Pacific Grove California 1994.
Course Description.
MA 5301 - Finite Groups and Finite Fields
Basic theory of finite groups (subgroups, normality, homomorphisms, abelian
groups, cyclic groups, commutators, order, cosets, index, conjugacy, simple
groups, Sylow Theorems), basic theory of finite fields (prime fields,
irreducible polynomials, Galois groups, trace), families of groups defined over
finite fields (linear groups).
Syllabus
We will discuss at least the following topics :
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Chapter 1: Definitions and Examples of Groups
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Chapter 2: Subgroups and Cosets
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Chapter 3: Homomorphisms
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Chapter 4: Group Actions
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Chapter 5: The Sylow Theorems and p-Groups
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Chapter 6: Permutation Groups
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Chapter 12: Rings, Ideals and Modules
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Chapter 16: Polynomial Rings, PIDs, and UFDs
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Chapter 17: Field Extensions
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Chapter 18: Galois Theory
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Chapter 20: Cyclotomy and Geometeric Constructions
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Chapter 21: Finite Fields
- Grading
Your grade will be based on 3 take home examinations.
a final examination.
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Start every written assignment at the top of a
new page, put your name at the beginning of each page and do not staple
different problems together. I expect the problems to be well written
in full English sentences with no gaps in detail or logic. Please
be as elegant and as concise as possible. Cite all references.