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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 36E
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ac9dc76-28dc-4d11-9e57-18b906b03777%2F09153bbd-65c2-495c-9308-89806ba036e0%2F1jhl51k_processed.jpeg&w=3840&q=75)
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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