In this problem, consider the group G = S3 acting on X = S4 by conjugation.In other words, given an element g E S3 (thought of as a permutation of {1, 2, 3})and an element x E S4 (thought of as a permutation of {1, 2, 3, 4}), the action isdefined byg •x = gxg¬!.For example, (12) · (34) = (12)(34)(12)-1 = (34).Answer the following, being sure to carefully justify your answers.(a) Describe the orbit Orbg((14)), and the stabiliser Stabg((14)).(b) Is the action faithful?(c) How many distinct orbits are there in X?

Answered: Image /qna-images/answer/7658ea82-cca3-4581-a6ac-31421f75c1fc.jpg

Answered: this problem, consider the group G = S3…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 16E: For an integer n1, let G=Un, the group of units in n that is, the set of all [ a ] in n that have...

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