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4. Consider the group A4, a group with twelve elements. Note that the positive divisors of 12 are 2, 3, 4, and 6 (along with 1 and 12). List the elements of A4, and write down the order of each element. List all the subgroups of A4 that have two elements. Include supporting discussion to you have not missed any subgroups. Same question for subgroups with three elements. Same question for subgroups with four elements. Same question for subgroups with six elements. (a) (b) prove that (c) (d) (e)

4. Consider the group A4, a group with twelve elements. Note that the positive divisors of 12 are 2, 3, 4, and 6 (along with 1 and 12). List the elements of A4, and write down the order of each element. List all the subgroups of A4 that have two elements. Include supporting discussion to you have not missed any subgroups. Same question for subgroups with three elements. Same question for subgroups with four elements. Same question for subgroups with six elements. (a) (b) prove that (c) (d) (e)

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.1: Definition Of A Group
Problem 14E: In Exercises 114, decide whether each of the given sets is a group with respect to the indicated...
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4. Consider the group A4, a group with twelve elements. Note that the positive divisors of 12 are 2, 3, 4, and 6 (along with 1 and 12). List the elements of A4, and write down the order of each element. (a) (b) List all the subgroups of A4 that have two elements. Include supporting discussion to prove that you have not missed any subgroups. (c) Same question for subgroups with three elements. (d) Same question for subgroups with four elements. Same question for subgroups with six elements. (e) 3
Transcribed Image Text:4. Consider the group A4, a group with twelve elements. Note that the positive divisors of 12 are 2, 3, 4, and 6 (along with 1 and 12). List the elements of A4, and write down the order of each element. (a) (b) List all the subgroups of A4 that have two elements. Include supporting discussion to prove that you have not missed any subgroups. (c) Same question for subgroups with three elements. (d) Same question for subgroups with four elements. Same question for subgroups with six elements. (e) 3
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