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(f) Write down, in cycle form, the elements of the cyclic subgroup H of So generated by p. (g) Write down, in cycle form, the elements of the conjugate subgroup roHor-¹.

(f) Write down, in cycle form, the elements of the cyclic subgroup H of So generated by p. (g) Write down, in cycle form, the elements of the conjugate subgroup roHor-¹.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 36E
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Parts (f) and (g)

The permutations p and q in Se have the two-line symbols 1 2 3 4 5 6 6) 4 6 2 1 5 3 p= and q = 1 2 3 4 5 6 1 5 2 3 4 6 6) (a) Write down the permutations p, q, p-¹ and q-1 in cycle form. (b) Write down the permutations po q and qop 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 Se have the two-line symbols 1 2 3 4 5 6 6) 4 6 2 1 5 3 p= and q = 1 2 3 4 5 6 1 5 2 3 4 6 6) (a) Write down the permutations p, q, p-¹ and q-1 in cycle form. (b) Write down the permutations po q and qop 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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