6. Show that a cycle of odd length is an even permutation, and a cycle of even length is an odd permutation. Hence determine which of the following members of S10 are even, or odd: (i) ( 193 ) ( 26 ) ( 4 5 10 ) (78) (ii) ( 19326 ) ( 4 5 10 78), (iii) ( 1932645 10).
6. Show that a cycle of odd length is an even permutation, and a cycle of even length is an odd permutation. Hence determine which of the following members of S10 are even, or odd: (i) ( 193 ) ( 26 ) ( 4 5 10 ) (78) (ii) ( 19326 ) ( 4 5 10 78), (iii) ( 1932645 10).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 56E
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Transcribed Image Text:6. Show that a cycle of odd length is an even permutation, and a cycle of even length is an odd
permutation. Hence determine which of the following members of S10 are even, or odd:
(i) ( 193 ) ( 26 ) ( 4 5 10 ) (78)
(ii) ( 19326 ) ( 4
5 10 78),
(iii) ( 1932645 10).
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