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ToT. (o and 8 are called conjugate elements) Let o,TE Sn. Define 6 = Show that if o (i) = j, then 6 = (t(i)) = T(j). (a) (b) Explain that the previous part says that if you apply T to each of the entries in the cycle notation of o, then you get the cycle notation for ô. In other words, if o has cycle decomposition (а, а .. ак, )(b bz ... bk,).... Then 8 has cycle decomposition (143 8) (2 6 5), (163) 7 5 2), Illustrate the previous part by letting (c) σ Ξ and quickly writing down the cycle decomposition for toT1. Check your

ToT. (o and 8 are called conjugate elements) Let o,TE Sn. Define 6 = Show that if o (i) = j, then 6 = (t(i)) = T(j). (a) (b) Explain that the previous part says that if you apply T to each of the entries in the cycle notation of o, then you get the cycle notation for ô. In other words, if o has cycle decomposition (а, а .. ак, )(b bz ... bk,).... Then 8 has cycle decomposition (143 8) (2 6 5), (163) 7 5 2), Illustrate the previous part by letting (c) σ Ξ and quickly writing down the cycle decomposition for toT1. Check your

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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ToT. (o and 8 are called conjugate elements) Let o,TE Sn. Define 6 = Show that if o (i) = j, then 6 = (t(i)) = T(j). (a) (b) Explain that the previous part says that if you apply T to each of the entries in the cycle notation of o, then you get the cycle notation for ô. In other words, if o has cycle decomposition (а, а .. ак, )(b bz ... bk,).... Then 8 has cycle decomposition (143 8) (2 6 5), (163) 7 5 2), Illustrate the previous part by letting (c) σ Ξ and quickly writing down the cycle decomposition for toT1. Check your
Transcribed Image Text:ToT. (o and 8 are called conjugate elements) Let o,TE Sn. Define 6 = Show that if o (i) = j, then 6 = (t(i)) = T(j). (a) (b) Explain that the previous part says that if you apply T to each of the entries in the cycle notation of o, then you get the cycle notation for ô. In other words, if o has cycle decomposition (а, а .. ак, )(b bz ... bk,).... Then 8 has cycle decomposition (143 8) (2 6 5), (163) 7 5 2), Illustrate the previous part by letting (c) σ Ξ and quickly writing down the cycle decomposition for toT1. Check your
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