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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 ...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;

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.1: Finite Permutation Groups
Problem 2E: Exercises 2. Express each permutation as a product of disjoint cycles and find the orbits of each...
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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,
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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