Contemporary Abstract Algebra9th EditionJoseph Gallian Publisher: Cengage Learning USISBN: 9781337249560
Contemporary Abstract Algebra
Solutions for Contemporary Abstract Algebra
Problem 2E:
Let [1234567823451786]and=[1234567813876524] . Write , , and as a. products of disjoint cycles; b....Problem 3E:
Write each of the following permutations as a product of disjointcycles. a. (1235)(413) b....Problem 4E:
Find the order of each of the following permutations. a. (14) b. (147) c. (14762) d. (a1a2...ak)Problem 5E:
What is the order of each of the following permutations? a. (124)(357) b. (124)(3567) c. (124)(35)...Problem 6E:
What is the order of each of the following permutations? [123456215463] [12345677612345]Problem 8E:
Determine whether the following permutations are even or odd. a. (135) b. (1356) c. (13567) d....Problem 9E:
What are the possible orders for the elements of S6andA6 ? Whatabout A7 ? (This exercise is referred...Problem 10E:
Show that A8 contains an element of order 15.Problem 11E:
Find an element in A12 of order 30.Problem 12E:
Show that a function from a finite set S to itself is one-to-one if and onlyif it is onto. Is this...Problem 14E:
Suppose that is a 6-cycle and is a 5-cycle. Determine whether 54135 is even or odd. Show your...Problem 18E:
In Sn , let be an r-cycle, an s-cycle, and a t-cycle. Completethe following statements: is even...Problem 19E:
Let and belong to Sn . Prove that is even if and only if and are both even or both odd.Problem 20E:
Associate an even permutation with the number +1 and an odd permutationwith the number -1. Draw an...Problem 21E:
Complete the following statement: A product of disjoint cycles iseven if and only if _________.Problem 22E:
What cycle is (a1a2an)1 ?Problem 23E:
Show that if H is a subgroup of Sn , then either every member of H isan even permutation or exactly...Problem 28E:
How many elements of order 5 are in S7 ?Problem 32E:
My mind rebels at stagnation. Give me problems, give me work, give me the most obtuse cryptogram, or...Problem 33E:
Let (a1a2a3a4)and(a5a6) be disjoint cycles in S10 . Show that there isno element x in S10 such that...Problem 38E:
Let H=S5(1)=1and(3)=3 . Prove that H is a subgroupof S5 . How many elements are in H? Is your...Problem 42E:
Represent the symmetry group of an equilateral triangle as a groupof permutations of its vertices...Problem 43E:
Prove that Sn is non-Abelian for all n3 .Problem 44E:
Prove that An is non-Abelian for all n4 .Problem 45E:
For n3 , let H=bSn(1)=1 or 2 and (2)=1or2 .Prove that H is a subgroup of Sn. Determine |H|.Problem 46E:
Show that in S7 , the equation x2=(1234) has no solutions but theequation x3=(1234) has at least...Problem 47E:
If (ab) and (cd) are distinct 2-cycles in Sn , prove that (ab) and (cd)commute if and only if they...Problem 49E:
Viewing the members of D4 as a group of permutations of a squarelabeled 1, 2, 3, 4 as described in...Problem 50E:
Viewing the members of D5 as a group of permutations of a regularpentagon with consecutive vertices...Problem 53E:
Show that A5 has 24 elements of order 5, 20 elements of order 3, and15 elements of order 2. (This...Problem 54E:
Find a cyclic subgroup of A8 that has order 4. Find a noncyclic subgroupof A8 that has order 4.Problem 57E:
Show that every element in An for n3 can be expressed as a3-cycle or a product of 3-cycles.Problem 58E:
Show that for n3,Z(Sn)=[] .Problem 62E:
(Indiana College Mathematics Competition) A card-shuffling machinealways rearranges cards in the...Problem 64E:
Find five subgroups of S5 of order 24.Problem 65E:
Why does the fact that the orders of the elements of A4 are 1, 2, and3 imply that Z(A4)=1 ?Problem 66E:
Let a belong to Sn . Prove that divides n!Browse All Chapters of This Textbook
Chapter 0 - PreliminariesChapter 1 - Introduction To GroupsChapter 2 - GroupsChapter 3 - Finite Groups; SubgroupsChapter 4 - Cyclic GroupsChapter 5 - Permutation GroupsChapter 6 - IsomorphismsChapter 7 - Cosets And Lagrange’s TheoremChapter 9 - Normal Subgroups And Factor GroupsChapter 10 - Group Homomorphisms
Chapter 12 - Introduction To RingsChapter 13 - Integral DomainsChapter 14 - Ideals And Factor RingsChapter 18 - Divisibility In Integral DomainsChapter 20 - Extension FieldsChapter 26 - Generators And RelationsChapter 28 - Frieze Groups And Crystallographic GroupsChapter 30 - Cayley Digraphs Of Groups
Sample Solutions for this Textbook
We offer sample solutions for Contemporary Abstract Algebra homework problems. See examples below:
Chapter 0, Problem 1EGiven: An equilateral triangle. Calculation: Three rotations at 0, 120 and 240 gives the symmetric...Chapter 2, Problem 1EChapter 3, Problem 1EChapter 4, Problem 1EChapter 5, Problem 1EGiven information: Concept used: Isomorphism: - A homomorphism ϕ from G into G¯ is said to be an...Chapter 7, Problem 1EChapter 9, Problem 1E
More Editions of This Book
Corresponding editions of this textbook are also available below:
Contemporary Abstract Algebra.
6th Edition
ISBN: 9780618514717
EBK CONTEMPORARY ABSTRACT ALGEBRA
8th Edition
ISBN: 9780100453074
Contemporary Abstract Algebra
8th Edition
ISBN: 9781133599708
Contemporary Abstract Algebra
8th Edition
ISBN: 9781285402734
Contemporary Abstract Algebra
8th Edition
ISBN: 9788131520741
Student Solutions Manual For Gallian's Contemporary Abstract Algebra, 8th
8th Edition
ISBN: 9781133608530
EBK CONTEMPORARY ABSTRACT ALGEBRA
8th Edition
ISBN: 8220100453076
Contemporary Abstract Algebra, 7th Edition
7th Edition
ISBN: 9780547165097
Student Solutions Manual For Gallian's Contemporary Abstract Algebra, 7th (students Solutions Manual)
7th Edition
ISBN: 9780547165394
Student Solutions Manual for Gallian's Contemporary Abstract Algebra, 9th
9th Edition
ISBN: 9781305657977
Contemporary Abstract Algebra
9th Edition
ISBN: 9781305657960
Bundle: Contemporary Abstract Algebra, 9th + Student Solutions Manual
9th Edition
ISBN: 9781337501590
EBK CONTEMPORARY ABSTRACT ALGEBRA
9th Edition
ISBN: 8220101434852
EBK CONTEMPORARY ABSTRACT ALGEBRA
9th Edition
ISBN: 9781305887855
Contemporary Abstract Algebra
5th Edition
ISBN: 9780618122141
Contemporary Abstract Algebra
10th Edition
ISBN: 9781000337358
CONTEMPORARY ABSTRACT ALGEBRA
10th Edition
ISBN: 9780367651787
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