Find the cycle of decomposition of o.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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need help with 4e please

4. Consider o =
(123)(45)(761) in S,
(a) Find the cycle of decomposition of o.
2 3 4 5
6 7
= (176 2 3)(4 5)
3
1
5 4 2
(b) Find o-1.
o-1 = (3 2 6 7 1)(4 5)
(c) Express o as a product of transpositions.
Using the cycle of decomposition in a)
(13)(12)(16)(17)(45)
(d) Find the order of o.
The cycle type here is the unordered integer partition 7 = 5 + 2.\
The order of the permutation o is lcm 5,2 = 10
(e) For this o, write down the set 2 and its partition into equivalence classes for the
equivalence relation defined below..
Let 2 be a nonempty set and o a permutation of 2. Define a relation
a-b if and only if b = o"(a) for some n E Z.
on 2 as follows:
Transcribed Image Text:4. Consider o = (123)(45)(761) in S, (a) Find the cycle of decomposition of o. 2 3 4 5 6 7 = (176 2 3)(4 5) 3 1 5 4 2 (b) Find o-1. o-1 = (3 2 6 7 1)(4 5) (c) Express o as a product of transpositions. Using the cycle of decomposition in a) (13)(12)(16)(17)(45) (d) Find the order of o. The cycle type here is the unordered integer partition 7 = 5 + 2.\ The order of the permutation o is lcm 5,2 = 10 (e) For this o, write down the set 2 and its partition into equivalence classes for the equivalence relation defined below.. Let 2 be a nonempty set and o a permutation of 2. Define a relation a-b if and only if b = o"(a) for some n E Z. on 2 as follows:
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