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Exercise 14.5.3. Using “switchyard", we proved that S, is generated by the permutations (12) and (12...n). Prove that the group Sn is generated by the following sets of permutations. 1. (12), (13),..., (1n) 2. (12), (23),..., (п — 1, п)

Exercise 14.5.3. Using “switchyard", we proved that S, is generated by the permutations (12) and (12...n). Prove that the group Sn is generated by the following sets of permutations. 1. (12), (13),..., (1n) 2. (12), (23),..., (п — 1, п)

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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What we have shown in the previous exercise is that the two permuta- tions r and t generate the group Sn. In other words, all of the information contained in the huge and complicated group S, is characterized in just two permutations! The study of group generators is an important part of group theory, but unfortunately it is beyond the level of this course. Exercise 14.5.3. Using "switchyard", we proved that S, is generated by the permutations (12) and (12...n). Prove that the group Sn is generated by the following sets of permutations. 1. (12), (13), ... , (1п) 2. (12), (23), ..., (п — 1, п)
Transcribed Image Text:What we have shown in the previous exercise is that the two permuta- tions r and t generate the group Sn. In other words, all of the information contained in the huge and complicated group S, is characterized in just two permutations! The study of group generators is an important part of group theory, but unfortunately it is beyond the level of this course. Exercise 14.5.3. Using "switchyard", we proved that S, is generated by the permutations (12) and (12...n). Prove that the group Sn is generated by the following sets of permutations. 1. (12), (13), ... , (1п) 2. (12), (23), ..., (п — 1, п)
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