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Consider the set of permutations V = {(1), (1 2) (3 4), (1 3) (2 4), (1 4) (2 3)}. Determine whether V forms a group under the operation of composition. If it is a group, is the group cyclic? If it is a group, is the group abelian?

Consider the set of permutations V = {(1), (1 2) (3 4), (1 3) (2 4), (1 4) (2 3)}. Determine whether V forms a group under the operation of composition. If it is a group, is the group cyclic? If it is a group, is the group abelian?

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.7: Direct Sums (optional)
Problem 23E: Prove that if r and s are relatively prime positive integers, then any cyclic group of order rs is...
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Consider the set of permutations V = {(1), (1 2) (3 4), (1 3) (2 4), (1 4) (2 3)}. Determine whether V forms a group under the operation of composition. If it is a group, is the group cyclic? If it is a group, is the group abelian?
Transcribed Image Text:Consider the set of permutations V = {(1), (1 2) (3 4), (1 3) (2 4), (1 4) (2 3)}. Determine whether V forms a group under the operation of composition. If it is a group, is the group cyclic? If it is a group, is the group abelian?
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