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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.

(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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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PROB 3 Part c

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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 lighten the notations, we denote by r the transposition (1 2) € S5.
Transcribed Image Text: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 lighten the 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 permutations in S, that commute with 7 and the the number of permutations in S, that commute with f(T) are equal.
Transcribed Image Text:(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 7 and the the number of permutations in S, that commute with f(T) are equal.
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