The permutations p= p and q in So have the two-line symbols 1 2 3 4 5 6 15 2 3 4 6 1 2 3 4 5 6 4 6 2 1 5 3 and q = (a) Write down the permutations p, q, p and q¹ in cycle form. (b) Write down the permutations poq 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.

The permutations p= p and q in So have the two-line symbols 1 2 3 4 5 6 15 2 3 4 6 1 2 3 4 5 6 4 6 2 1 5 3 and q = (a) Write down the permutations p, q, p and q¹ in cycle form. (b) Write down the permutations poq 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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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