3. Let a and ẞ be permutations in S11 with a = (7 4 1 3) (28) (5) (9 6 10 11), β = ( 1 2 3 8 7 10 4 5 6 1 6 7 8 9 10 11 5 11 4 239 (a) Express ẞ as a composition of disjoint cycles. (b) Find the fixed points of ẞ². (c) Express a oẞ as a composition of disjoint cycles. (d) Find the orders of a and B. [1] [1] [1] [2] (e) Determine whether a is an even or odd permutation, explaining your rea- soning clearly. [2] (f) Find S11 such that Boy = a, showing your reasoning clearly. [3]
3. Let a and ẞ be permutations in S11 with a = (7 4 1 3) (28) (5) (9 6 10 11), β = ( 1 2 3 8 7 10 4 5 6 1 6 7 8 9 10 11 5 11 4 239 (a) Express ẞ as a composition of disjoint cycles. (b) Find the fixed points of ẞ². (c) Express a oẞ as a composition of disjoint cycles. (d) Find the orders of a and B. [1] [1] [1] [2] (e) Determine whether a is an even or odd permutation, explaining your rea- soning clearly. [2] (f) Find S11 such that Boy = a, showing your reasoning clearly. [3]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![3. Let a and ẞ be permutations in S11 with
a = (7 4 1 3) (28) (5) (9 6 10 11),
β
=
(
1 2 3
8 7 10
4 5
6 1
6
7 8 9 10 11
5 11 4 239
(a) Express ẞ as a composition of disjoint cycles.
(b) Find the fixed points of ẞ².
(c) Express a oẞ as a composition of disjoint cycles.
(d) Find the orders of a and B.
[1]
[1]
[1]
[2]
(e) Determine whether a is an even or odd permutation, explaining your rea-
soning clearly.
[2]
(f) Find S11 such that Boy = a, showing your reasoning clearly.
[3]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56349570-c850-4378-b43a-2d1a85030776%2Fc8ee0d78-d04a-428b-8d4e-a87e12e74aad%2F8enswi_processed.png&w=3840&q=75)
Transcribed Image Text:3. Let a and ẞ be permutations in S11 with
a = (7 4 1 3) (28) (5) (9 6 10 11),
β
=
(
1 2 3
8 7 10
4 5
6 1
6
7 8 9 10 11
5 11 4 239
(a) Express ẞ as a composition of disjoint cycles.
(b) Find the fixed points of ẞ².
(c) Express a oẞ as a composition of disjoint cycles.
(d) Find the orders of a and B.
[1]
[1]
[1]
[2]
(e) Determine whether a is an even or odd permutation, explaining your rea-
soning clearly.
[2]
(f) Find S11 such that Boy = a, showing your reasoning clearly.
[3]
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