#3. Thanks. 3. List all of the permutations of S4. Find each of the following sets:a) {o € S4: 0(1) = 3}b) {0 € S₁:0 (2) = 2}c) {0 € S4:0 (1) = 3 and o(2) = 2}Are any of these sets subgroups of S4? Justify your conclusions! (5 from 5.4)

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Answered: 3. List all of the permutations of S4.…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 37E

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3. List all of the permutations of S4. Find each of the following sets: a) {0 € S4:0 (1) = 3} b) {0 € S4:0 (2) = 2} c) {0 € S4:0(1) = 3 and o(2) = 2} Are any of these sets subgroups of S4? Justify your conclusions! (5 from 5.4)