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The permutations p= p and q in Se have the two-line symbols 1 2 3 4 5 6 4 621 5 3 and q= 1 2345 1 5 2 3 4 (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,poq 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 So 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 So generated by p. (g) Write down, in cycle form, the elements of the conjugate subgroup roHor-¹.

The permutations p= p and q in Se have the two-line symbols 1 2 3 4 5 6 4 621 5 3 and q= 1 2345 1 5 2 3 4 (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,poq 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 So 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 So generated by p. (g) Write down, in cycle form, the elements of the conjugate subgroup roHor-¹.

Advanced Engineering Mathematics
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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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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