b. For each of the following, show that G is a group using the operation of S4,and determine how many elements of g of G satisfy g² = e.i.G = {e, (12)(34), (13)(24), (14)(23)}ii.G = {e, (1234), (13)(24), (1432)}

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Answered: b. For each of the following, show that…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 13E: Exercises 13. For each of the following values of, find all subgroups of the group described in...

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b. For each of the following, show that G is a group using the operation of S4, and determine how many elements of g of G satisfy g² = e. i. G= {e, (12)(34), (13)(24), (14)(23)} ii. G = {e, (1234), (13)(24), (1432)}