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Example 7: Check whether or not 0: A, → R" : 0(p) = p(n) is a representation of A,. Solution: Though 0 is well-defined, it need not be a homomorphism (13)(2 For example, if n=5, p, = (1 2 3), p2 = (1 2 5), then p,p2 = (15) (2 3). So e(p, P2) =1. But 0(p,)(p,)=5. Thus, 0 is not a representation of A,. OY IS it %3D %3D

Example 7: Check whether or not 0: A, → R" : 0(p) = p(n) is a representation of A,. Solution: Though 0 is well-defined, it need not be a homomorphism (13)(2 For example, if n=5, p, = (1 2 3), p2 = (1 2 5), then p,p2 = (15) (2 3). So e(p, P2) =1. But 0(p,)(p,)=5. Thus, 0 is not a representation of A,. OY IS it %3D %3D

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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Example 7: Check whether or not 0: A, -> R* : 0(p) = p(n) is a representation of A,. Solution: Though 0 is well-defined, it need not be a homomorphism (13)(2) For example, if n=5, p, = (1 2 3), P2 = (1 2 5), then P,P2 = (15) (2 3). So e(p, P2) =1. But 0(p,)(p,)=5. Thus, 0 is not a representation of A,. 77 OY IS it %3D %3D
Transcribed Image Text:Example 7: Check whether or not 0: A, -> R* : 0(p) = p(n) is a representation of A,. Solution: Though 0 is well-defined, it need not be a homomorphism (13)(2) For example, if n=5, p, = (1 2 3), P2 = (1 2 5), then P,P2 = (15) (2 3). So e(p, P2) =1. But 0(p,)(p,)=5. Thus, 0 is not a representation of A,. 77 OY IS it %3D %3D
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