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(g) Write down, in cycle form, the elements of the conjugate subgroup ro Hor-¹.

(g) Write down, in cycle form, the elements of the conjugate subgroup ro Hor-¹.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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Part g please
The permutations p and q in So have the two-line symbols 1 2 3 4 5 6 4 6 2 15 3, (3) 1 2 3 4 5 6 1 5 2 3 4 6 P = and q = (a) Write down the permutations p, q, p and q¹ in cycle form. (b) Write down the permutations po q and q o p in cycle form. (c) Write down the orders of p, q, po q and qop. (d) Write down p and q as composites of transpositions, and state the parity of p and the parity of q. (e) Let r be the permutation in S6 whose cycle form is (4 6 5). Write down, in cycle form, the permutation t=ropor-¹ (the conjugate of p by r). (f) Write down, in cycle form, the elements of the cyclic subgroup H of S6 generated by p. (g) Write down, in cycle form, the elements of the conjugate subgroup roHor-¹.
Transcribed Image Text:The permutations p and q in So have the two-line symbols 1 2 3 4 5 6 4 6 2 15 3, (3) 1 2 3 4 5 6 1 5 2 3 4 6 P = and q = (a) Write down the permutations p, q, p and q¹ in cycle form. (b) Write down the permutations po q and q o p in cycle form. (c) Write down the orders of p, q, po q and qop. (d) Write down p and q as composites of transpositions, and state the parity of p and the parity of q. (e) Let r be the permutation in S6 whose cycle form is (4 6 5). Write down, in cycle form, the permutation t=ropor-¹ (the conjugate of p by r). (f) Write down, in cycle form, the elements of the cyclic subgroup H of S6 generated by p. (g) Write down, in cycle form, the elements of the conjugate subgroup roHor-¹.
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