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Exercise 10.2. Let a = (a₁ a₂...an) be an n-cycle in Sym(m) show that there is an element 3 such that a = 3(1 2 3 ...n)B-¹. Hint: start from the injection given by i goes to a; and extend this to a bijection [m] → [m]. Show that this bijection satisfies the above.

Exercise 10.2. Let a = (a₁ a₂...an) be an n-cycle in Sym(m) show that there is an element 3 such that a = 3(1 2 3 ...n)B-¹. Hint: start from the injection given by i goes to a; and extend this to a bijection [m] → [m]. Show that this bijection satisfies the above.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 56E
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This is a group theory question, please explain it using simple words step by step, thanks :)

Exercise 10.2. Let a = (a₁ a₂...an) be an n-cycle in Sym(m) show that there is an element 3 such that a = 3(1 2 3 ...n)B-¹. Hint: start from the injection given by i goes to a; and extend this to a bijection [m] → [m]. Show that this bijection satisfies the above.
Transcribed Image Text:Exercise 10.2. Let a = (a₁ a₂...an) be an n-cycle in Sym(m) show that there is an element 3 such that a = 3(1 2 3 ...n)B-¹. Hint: start from the injection given by i goes to a; and extend this to a bijection [m] → [m]. Show that this bijection satisfies the above.
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