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. aHHa where H is any...Problem 2TFE:
True or False
Label each of the following statements as either true or false.
2. Let be any subgroup...Problem 3TFE:
True or False Label each of the following statements as either true or false. Let H be any subgroup...Problem 4TFE:
True or False
Label each of the following statements as either true or false.
4. The elements of...Problem 5TFE:
True or False Label each of the following statements as either true or false. The order of an...Problem 6TFE:
True or False
Label each of the following statements as either true or false.
The order of any...Problem 7TFE:
True or False Label each of the following statements as either true or false. Let H be a subgroup of...Problem 8TFE:
True or False
Label each of the following statements as either true or false.
8. Every left coset of...Problem 1E:
1. Consider , the groups of units in under multiplication. For each of the following subgroups in ,...Problem 2E:
For each of the following subgroups H of the addition groups Z18, find the distinct left cosets of H...Problem 3E:
In Exercises 3 and 4, let G be the octic group D4=e,,2,3,,,, in Example 12 of section 4.1, with its...Problem 4E:
In Exercises 3 and 4, let be the octic group in Example 12 of section 4.1, with its multiplication...Problem 5E:
Let H be the subgroup (1),(1,2) of S3. Find the distinct left cosets of H in S3, write out their...Problem 6E:
Let be the subgroup of .
Find the distinct left cosets of in , write out their elements,...Problem 7E:
In Exercises 7 and 8, let be the multiplicative group of permutation matrices in Example 6 of...Problem 11E:
Let be a group of order 24. If is a subgroup of , what are all the possible orders of ?
Problem 12E:
Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order...Problem 13E:
Let H be a subgroup of the group G. Prove that if two right cosets Ha and Hb are not disjoint, then...Problem 14E:
Let H be a subgroup of a group G. Prove that gHg1 is a subgroup of G for any gG.We say that gHg1 is...Problem 16E:
Let H be a subgroup of the group G. Prove that the index of H in G is the number of distinct right...Problem 17E:
Show that a group of order 4 either is cyclic or is isomorphic to the Klein four group e,a,b,ab=ba.Problem 19E:
Find the order of each of the following elements in the multiplicative group of units .
for
for
...Problem 20E:
Find all subgroups of the octic group D4.Problem 22E:
Lagranges Theorem states that the order of a subgroup of a finite group must divide the order of the...Problem 23E:
Find all subgroups of the quaternion group.Problem 24E:
Find two groups of order 6 that are not isomorphic.Problem 25E:
If H and K are arbitrary subgroups of G, prove that HK=KH if and only if HK is a subgroup of G.Problem 26E:
Let p be prime and G the multiplicative group of units Up=[a]Zp[a][0]. Use Lagranges Theorem in G to...Problem 27E:
Prove that any group with prime order is cyclic.Problem 28E:
Let G be a group of order pq, where p and q are primes. Prove that any nontrivial subgroup of G is...Problem 29E:
Let be a group of order , where and are distinct prime integers. If has only one subgroup of...Problem 30E:
Let G be an abelian group of order 2n, where n is odd. Use Lagranges Theorem to prove that G...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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