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Abstract Algebra:
PRETEXT XML SAMPLE ONLY
Thomas W. Judson, Isaac Newton (Editor)
Contents
Index
Prev
Up
Next
Contents
Prev
Up
Next
Front Matter
Colophon
Author Biography
About Robert A. Beezer
Dedication
Acknowledgements
Preface
Contributors to the 4\(^\mathrm{th}\) Edition
I
Basics
1
Preliminaries
A Short Note on Proofs
Sets and Equivalence Relations
Sage
Exercises
Sage Exercises
References and Suggested Readings
2
The Integers
Mathematical Induction
The Division Algorithm
Sage
Exercises
Programming Exercises
Sage Exercises
References and Suggested Readings
II
Algebra
3
Groups
Integer Equivalence Classes and Symmetries
Definitions and Examples
Subgroups
Sage
Exercises
Additional Exercises: Detecting Errors
Sage Exercises
References and Suggested Readings
4
Cyclicity
Cyclic groups
Subgroups of a Cyclic Group
Cyclic Groups of Complex Numbers
Large Powers of Integers
Exercises
Programming Exercises
Sage Exercises
References and Suggested Readings
Back Matter
A
Notation
B
Hints and Answers to Selected Odd Exercises
C
Hints and Answers to Selected Even Exercises
D
Hints and Answers to Selected Exercises
E
A Structured Appendix
A Section in an Appendix
Numbering in the Back Matter
F
GNU Free Documentation License
Index
Colophon
Authored in PreTeXt
Solutions
D
Hints and Answers to Selected Exercises
Part
I
Basics
Chapter
1
Preliminaries
Exercises
1.4
Exercises
Warm-up
1.4.2
.
Hint
.
1.4.6
.
Hint
.
1.4.10
.
Hint
.
1.4.14
.
Hint
.
More Exercises
1.4.18
.
Hint
.
1.4.20
.
Hint
.
1.4.22
.
Hint
.
1.4.24
.
Hint
.
1.4.28
.
Hint
.
Chapter
2
The Integers
Exercises
2.4
Exercises
2.4.1
.
Answer
.
2.4.3
.
Answer
.
2.4.9
.
Hint
.
2.4.11
.
Hint
.
2.4.17
.
Fibonacci Numbers.
Hint
.
2.4.19
.
Hint
.
2.4.23
.
Hint
.
2.4.27
.
Hint
.
2.4.29
.
Hint
.
Part
II
Algebra
Chapter
3
Groups
Exercises
3.5
Exercises
3.5.1
.
Hint
.
3.5.2
.
Hint
.
3.5.6
.
Hint
.
3.5.8
.
Hint
.
3.5.15
.
Hint
.
3.5.16
.
Hint
.
3.5.17
.
Hint
.
3.5.18
.
Hint
.
3.5.25
.
Hint
.
3.5.31
.
Hint
.
3.5.35
.
Hint
.
3.5.41
.
Hint
.
3.5.46
.
Hint
.
3.5.49
.
Hint
.
3.5.55
.
Answer
.
3.5.56
.
Answer
.
3.5.57
.
Answer
.
3.5.58
.
Answer
.
3.5.59
.
(a)
Answer
.
(b)
(i)
Answer
.
(ii)
Answer
.
3.5.60
.
(a)
Answer
.
(b)
(i)
Answer
.
(ii)
Answer
.
