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Solutions B Hints and Answers to Selected Exercises

Chapter 1 Preliminaries
Exercises 1.4 Exercises
Chapter 2 The Integers
Exercises 2.4 Exercises
2.4.17. Fibonacci Numbers.
Hint.
Chapter 3 Groups
Exercises 3.5 Exercises
Chapter 4 Cyclic Groups
Exercises 4.5 Exercises
Chapter 5 Permutation Groups
Exercises 5.4 Exercises
Chapter 6 Cosets and Lagrange's Theorem
Exercises 6.5 Exercises
Chapter 7 Introduction to Cryptography
Exercises 7.4 Exercises
Chapter 8 Algebraic Coding Theory
Exercises 8.6 Exercises
Chapter 9 Isomorphisms
Exercises 9.4 Exercises
Chapter 10 Normal Subgroups and Factor Groups
Exercises 10.4 Exercises
Chapter 11 Homomorphisms
Exercises 11.4 Exercises
Chapter 12 Matrix Groups and Symmetry
Exercises 12.4 Exercises
Chapter 13 The Structure of Groups
Exercises 13.4 Exercises
Chapter 14 Group Actions
Exercises 14.5 Exercises
Chapter 15 The Sylow Theorems
Exercises 15.4 Exercises
Chapter 16 Rings
Exercises 16.7 Exercises
Chapter 17 Polynomials
Exercises 17.5 Exercises
17.5.20. Cyclotomic Polynomials.
Hint.
Chapter 18 Integral Domains
Exercises 18.4 Exercises
Chapter 19 Lattices and Boolean Algebras
Exercises 19.5 Exercises
Chapter 20 Vector Spaces
Exercises 20.5 Exercises
20.5.15. Linear Transformations.
Hint.
Chapter 21 Fields
Exercises 21.5 Exercises
Chapter 22 Finite Fields
Exercises 22.4 Exercises
22.4.24. Wilson's Theorem.
Hint.
Chapter 23 Galois Theory
Exercises 23.5 Exercises