If o is a k-cycle then the order of o is k. On the otherhand, if 7 is a product of disjoint cycles o1, 02, 03 ...0m such that the order of a, is k; then the order of 7 is given by lcm(k, k2, k3, ..., km). Find the order each of the following. (a) (132 4) € S. (b) (1 4 3)(2 5 6 7) e Sr. (c) (1 43 6)(2 9)(5 7 8) e Sp. (d) (1 7)(2 6)(3 5 4) (1 2 3)(4 5 6 7) e S;
If o is a k-cycle then the order of o is k. On the otherhand, if 7 is a product of disjoint cycles o1, 02, 03 ...0m such that the order of a, is k; then the order of 7 is given by lcm(k, k2, k3, ..., km). Find the order each of the following. (a) (132 4) € S. (b) (1 4 3)(2 5 6 7) e Sr. (c) (1 43 6)(2 9)(5 7 8) e Sp. (d) (1 7)(2 6)(3 5 4) (1 2 3)(4 5 6 7) e S;
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 31E
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![If o is a k-cycle then the order of o is k. On the otherhand, if 7 is a product of
disjoint cycles o1, 02, 03 .m such that the order of o; is k; then the order of 7 is
given by lem(k1, k2, kg, ..., km). Find the order each of the following.
(a) (1 32 4) e S4.
(b) (1 4 3)(2 5 6 7) E S7.
(c) (1 43 6)(2 9)(5 7 8) E Sg.
(d) (1 7)(2 6)(3 5 4) o (1 2 3)(4 5 6 7) e S,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6ec8d8c-852f-4b9e-ad7a-66a2ac9fd1f9%2Fd6b1b1b3-5bb1-4483-9181-ec2b2b100e1d%2Fbm1i6o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If o is a k-cycle then the order of o is k. On the otherhand, if 7 is a product of
disjoint cycles o1, 02, 03 .m such that the order of o; is k; then the order of 7 is
given by lem(k1, k2, kg, ..., km). Find the order each of the following.
(a) (1 32 4) e S4.
(b) (1 4 3)(2 5 6 7) E S7.
(c) (1 43 6)(2 9)(5 7 8) E Sg.
(d) (1 7)(2 6)(3 5 4) o (1 2 3)(4 5 6 7) e S,
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