ELEMENTS OF MODERN ALGEBRA8th EditionGilbert Publisher: CENGAGE LISBN: 9780357671139
ELEMENTS OF MODERN ALGEBRA
Solutions for ELEMENTS OF MODERN ALGEBRA
Problem 1TFE:
True or False
Label each of the following statements as either true or false.
1. Every permutation...Problem 2TFE:
True or False
Label each of the following statements as either true or false.
2. A permutation can...Problem 3TFE:
True or False
Label each of the following statements as either true or false.
3. The product of...Problem 4TFE:
True or False Label each of the following statements as either true or false. Disjoint cycles...Problem 5TFE:
True or False
Label each of the following statements as either true or false.
5. The identity...Problem 6TFE:
True or False
Label each of the following statements as either true or false.
6. Every permutation...Problem 7TFE:
True or False Label each of the following statements as either true or false. An r-cycle is an even...Problem 8TFE:
True or False
Label each of the following statements as either true or false.
8. The set of all odd...Problem 9TFE:
True or False
Label each of the following statements as either true or false.
9. The symmetric...Problem 10TFE:
True or False
Label each of the following statements as either true or false.
10. A transposition...Problem 11TFE:
True or False
Label each of the following statements as either true or false.
11. The order of an...Problem 12TFE:
True or False
Label each of the following statements as either true or false.
12. The mutually...Problem 1E:
Exercises
1. Express each permutation as a product of disjoint cycles and find the orbits of each...Problem 2E:
Exercises
2. Express each permutation as a product of disjoint cycles and find the orbits of each...Problem 3E:
Exercises
3. In each part of Exercise , decide whether the permutation is even or odd.
1. Express...Problem 4E:
In each part of Exercise 2, decide whether the permutation is even or odd. Express each permutation...Problem 5E:
Find the order of each permutation in Exercise 1. Express each permutation as a product of disjoint...Problem 6E:
Exercises
6. Find the order of each permutation in Exercise .
2. Express each permutation as a...Problem 7E:
Exercises
7. Express each permutation in Exercise as a product of transpositions.
1. Express each...Problem 8E:
Express each permutation in Exercise 2 as a product of transpositions. Express each permutation as a...Problem 9E:
Compute f2, f3, and f1 for each of the following permutations. a. f=(1,5,2,4) b. f=(2,7,4,3,5) c....Problem 10E:
Let f=(1,2,3)(4,5). Compute each of the following powers of f. a. f1 b. f18 c. f23 d. f201Problem 11E:
Exercises Let f=(1,6)(2,3,5,4). Compute each of the following powers of f. a. f1 b. f12 c. f103 d....Problem 13E:
Exercises
13. For the given permutations, and , find a permutation such that is the conjugate of ...Problem 14E:
Exercises
14. Write the permutation as a product of a permutation of order and a permutation of...Problem 15E:
Exercises
15. Write the permutation as a product of a permutation of order and of order .
Problem 16E:
Exercises List all the elements of the alternating group A3, written in cyclic notation.Problem 20E:
Exercises Construct a multiplication table for the octic group D4 described in Example 12 of this...Problem 21E:
Exercises
21. Find all the distinct cyclic subgroups of the octic group in Exercise .
20. Construct...Problem 22E:
Exercises Find an isomorphism from the octic group D4 in Example 12 of this section to the group...Problem 24E:
Exercises In Section 3.3, the centralizer of an element a in the group G was shown to be the...Problem 32E:
Exercises Prove that the order of An is n!2.Browse All Chapters of This Textbook
Chapter 1.1 - SetsChapter 1.2 - MappingsChapter 1.3 - Properties Of Composite Mappings (optional)Chapter 1.4 - Binary OperationsChapter 1.5 - Permutations And InversesChapter 1.6 - MatricesChapter 1.7 - RelationsChapter 2.1 - Postulates For The Integers (optional)Chapter 2.2 - Mathematical InductionChapter 2.3 - Divisibility
Chapter 2.4 - Prime Factors And Greatest Common DivisorChapter 2.5 - Congruence Of IntegersChapter 2.6 - Congruence ClassesChapter 2.7 - Introduction To Coding Theory (optional)Chapter 2.8 - Introduction To Cryptography (optional)Chapter 3.1 - Definition Of A GroupChapter 3.2 - Properties Of Group ElementsChapter 3.3 - SubgroupsChapter 3.4 - Cyclic GroupsChapter 3.5 - IsomorphismsChapter 3.6 - HomomorphismsChapter 4.1 - Finite Permutation GroupsChapter 4.2 - Cayley’s TheoremChapter 4.3 - Permutation Groups In Science And Art (optional)Chapter 4.4 - Cosets Of A SubgroupChapter 4.5 - Normal SubgroupsChapter 4.6 - Quotient GroupsChapter 4.7 - Direct Sums (optional)Chapter 4.8 - Some Results On Finite Abelian Groups (optional)Chapter 5.1 - Definition Of A RingChapter 5.2 - Integral Domains And FieldsChapter 5.3 - The Field Of Quotients Of An Integral DomainChapter 5.4 - Ordered Integral DomainsChapter 6.1 - Ideals And Quotient RingsChapter 6.2 - Ring HomomorphismsChapter 6.3 - The Characteristic Of A RingChapter 6.4 - Maximal Ideals (optional)Chapter 7.1 - The Field Of Real NumbersChapter 7.2 - Complex Numbers And QuaternionsChapter 7.3 - De Moivre’s Theorem And Roots Of Complex NumbersChapter 8.1 - Polynomials Over A RingChapter 8.2 - Divisibility And Greatest Common DivisorChapter 8.3 - Factorization In F [x]Chapter 8.4 - Zeros Of A PolynomialChapter 8.5 - Solution Of Cubic And Quartic Equations By Formulas (optional)Chapter 8.6 - Algebraic Extensions Of A Field
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EBK ELEMENTS OF MODERN ALGEBRA
8th Edition
ISBN: 9780100475755
Elements Of Modern Algebra
8th Edition
ISBN: 9781285463230
EBK ELEMENTS OF MODERN ALGEBRA
8th Edition
ISBN: 8220100475757
Elements Of Modern Algebra
8th Edition
ISBN: 9781285965918
Elements of Modern Algebra
5th Edition
ISBN: 9780534373511
Elements of Modern Algebra
6th Edition
ISBN: 9780534402648
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