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GAP Exercises

Version 1.0

February 17, 2010

Stefan Kohl
Email: stefan@mcs.st-and.ac.uk
Homepage: http://www.gap-system.org/DevelopersPages/StefanKohl/
Address:
Department of Mathematics
University of Vlora
Lagjja: Pavaresia
Vlore / Albania

Contents

1 The Exercises

1.1 On Commutators and Derived Subgroups

1.1-1 Exercise
1.1-2 Hints

1.2 On Outer Automorphisms Fixing Conjugacy Classes

1.2-1 Exercise
1.2-2 Hints

1.3 Drawing the Ulam Spiral

1.3-1 Exercise
1.3-2 Hints

1.4 Automorphism Group of the Smallest Projective Plane

1.4-1 Exercise
1.4-2 Hints

1.5 Installing a Missing Method

1.5-1 Exercise
1.5-2 Hints

1.6 Finding Good abc Triples

1.6-1 Exercise
1.6-2 Hints

1.7 Automorphism Groups of Finite Graphs

1.7-1 Exercise
1.7-2 Hints

1.8 Enumerating Paths

1.8-1 Exercise
1.8-2 Hints

1.9 Wieferich Primes

1.9-1 Exercise
1.9-2 Hints

1.10 Counting Words in a File

1.10-1 Exercise
1.10-2 Hints

1.11 Non-Metabelian p-Groups

1.11-1 Exercise
1.11-2 Hints

1.12 The Growth of the Sum-of-Divisors Function

1.12-1 Exercise
1.12-2 Hints

1.13 Pell's Equation

1.13-1 Exercise
1.13-2 Hints

1.14 Automorphism Groups of Odd Order

1.14-1 Exercise
1.14-2 Hints

1.15 Composite Sums

1.15-1 Exercise
1.15-2 Hints

1.16 Rational Points on the Unit Sphere

1.16-1 Exercise
1.16-2 Hints

1.17 Aliquot Sequences

1.17-1 Exercise
1.17-2 Hints

1.18 The Q Sequence

1.18-1 Exercise
1.18-2 Hints

1.19 A Quickly Growing Function

1.19-1 Exercise
1.19-2 Hints

1.20 The 3n+1 Conjecture

1.20-1 Exercise
1.20-2 Hints

2 The Solutions

2.1 On Commutators and Derived Subgroups (Solution)

2.2 On Outer Automorphisms Fixing Conjugacy Classes (Solution)

2.3 Drawing the Ulam Spiral (Solution)

2.4 Automorphism Group of the Smallest Projective Plane (Solution)

2.5 Installing a Missing Method (Solution)

2.6 Finding Good abc Triples (Solution)

2.7 Automorphism Groups of Finite Graphs (Solution)

2.8 Enumerating Paths (Solution)

2.9 Wieferich Primes (Solution)

2.10 Counting Words in a File (Solution)

2.11 Non-Metabelian p-Groups (Solution)

2.12 The Growth of the Sum-of-Divisors Function (Solution)

2.13 Pell's Equation (Solution)

2.14 Automorphism Groups of Odd Order (Solution)

2.15 Composite Sums (Solution)

2.16 Rational Points on the Unit Sphere (Solution)

2.17 Aliquot Sequences (Solution)

2.18 The Q Sequence (Solution)

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