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Define o = (123)(456)(78) and 7 = (14)(2635)(89) in S9 (a) Write To as a product of disjoint cycles. (b) What is the order of To (c) Write To as a product of transpositions. (d) Is To even or odd?

Define o = (123)(456)(78) and 7 = (14)(2635)(89) in S9 (a) Write To as a product of disjoint cycles. (b) What is the order of To (c) Write To as a product of transpositions. (d) Is To even or odd?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 66E
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please just answer the last part (d). Thank you. 

Define \( \sigma = (123)(456)(78) \) and \( \tau = (14)(2635)(89) \) in \( S_9 \). (a) Write \( \tau \sigma \) as a product of disjoint cycles. (b) What is the order of \( \tau \sigma \)? (c) Write \( \tau \sigma \) as a product of transpositions. (d) Is \( \tau \sigma \) even or odd?
Transcribed Image Text:Define \( \sigma = (123)(456)(78) \) and \( \tau = (14)(2635)(89) \) in \( S_9 \). (a) Write \( \tau \sigma \) as a product of disjoint cycles. (b) What is the order of \( \tau \sigma \)? (c) Write \( \tau \sigma \) as a product of transpositions. (d) Is \( \tau \sigma \) even or odd?
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