PROB 3 Part cplz provide its handwritten answer asap Problem 3. The goal of this problem is to study the automorphisms of S, that is, the iso-morphisms from S5 to itself. Let f: S5 Ss be an automorphism. To lightenthe notations, we denote by r the transposition (1 2) € S5. (c) Show that a permutation o E S, commutes with r if and only if the permu-tation f(o) commutes with f(7). Deduce that the number of permutationsin S, that commute with 7 and the the number of permutations in S, thatcommute with f(T) are equal.

Answered: Image /qna-images/answer/5826ea73-d4ad-4103-abd1-c5fd5be54781.jpg

Answered: (c) Show that a permutation o E S,…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 4TFE: True or False Label each of the following statements as either true or false. 4. Any automorphism...

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(c) Show that a permutation o E S, commutes with r if and only if the permu- tation f(o) commutes with f(7). Deduce that the number of permutations in S, that commute with r and the the number of permutations in S, that commute with f(r) are equal.