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

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 13E: In Exercises and , part of the multiplication table for the group is given. In each case, complete...

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