Exercise 14.4.22. Let o be a permutation in S„. (a) Show that there exists an integer k >1 such that ok = o. (b) Show that there exists an integer l > 1 such that of = o-1. (c) Let K be the set of all...

Please do Exercise 14.4.22 and do all the parts. Please show step by step and explain

Exercise 14.4.22. Let o be a permutation in S„.<br>(a) Show that there exists an integer k >1 such that ok = o.<br>(b) Show that there exists an integer l > 1 such that of = o-1.<br>(c) Let K be the set of all integers k > 1 such that ok = o. Show that K<br>is an infinite set (that is, K has an infinite number of elements).<br>(d) Let L be the set of all integers e > 1 such that of = o-1. Show that L<br>is an infinite set.<br>= 0.<br>(e) What is the relationship between the sets K and L?<br>

Extracted text: Exercise 14.4.22. Let o be a permutation in S„. (a) Show that there exists an integer k >1 such that ok = o. (b) Show that there exists an integer l > 1 such that of = o-1. (c) Let K be the set of all integers k > 1 such that ok = o. Show that K is an infinite set (that is, K has an infinite number of elements). (d) Let L be the set of all integers e > 1 such that of = o-1. Show that L is an infinite set. = 0. (e) What is the relationship between the sets K and L?

Jun 05, 2022

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Exercise 14.4.22. Let o be a permutation in S„. (a) Show that there exists an integer k >1 such that ok = o. (b) Show that there exists an integer l > 1 such that of = o-1. (c) Let K be the set of all...

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