Prove that the mapping given in Example 11 is a homomorphism. I EXAMPLE 11 The mapping from S, to Z, that takes an even permutationto 0 and an odd permutation to 1 is a homomorphism. Figure 10.2 illus-trates the telescoping nature of the mapping.23)(13)(12)(123 132)(1)23)12)(13123Y132)(1)(12)(13)K32)923)932)(1)Figure 10.2 Homomorphism from S, to Z,.

To prove that the mapping from Sn (the symmetric group of degree n) to ℤ2 (the integers modulo 2),…

Answered: I EXAMPLE 11 The mapping from S, to Z,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Prove that the mapping given in Example 11 is a homomorphism.

I EXAMPLE 11 The mapping from S, to Z, that takes an even permutation
to 0 and an odd permutation to 1 is a homomorphism. Figure 10.2 illus-
trates the telescoping nature of the mapping.
23)
(13)
(12)
(123 132)
(1)
23)
12)
(13
123Y132)
(1)
(12)
(13)
K32)923)
932)
(1)
Figure 10.2 Homomorphism from S, to Z,.

Expert Solution

Step 1: Introduction

To prove that the mapping from S_n (the symmetric group of degree n) to ℤ₂ (the integers modulo 2), which assigns the value 0 to even permutations and 1 to odd permutations, is a homomorphism, we need to show that it preserves the group operation.

Step 2: Calculation

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