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Let T and (a bc) be permutations in a symmetric group Sn. Prove that T(a b c)t1(τ(α) +τ(b) + τ(c)

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I need help solving/ understanding attached for abstarct algebra dealing with permutations

 

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Let T and (a bc) be permutations in a symmetric group Sn. Prove that T(a b c)t1
(τ(α) +τ(b) + τ(c)
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Let T and (a bc) be permutations in a symmetric group Sn. Prove that T(a b c)t1 (τ(α) +τ(b) + τ(c)

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Step 1

To prove the property of conjugation of a 3-cycle in the Symmetric group

Step 2

Problem statement (note the correction , there is no + sign; it doesnt make any sense). For convenience, we will denote tau as T, in what follows.

Let r E S, be any permutation
(a b c) e S be any 3-cycle.
72
То prove
7(abe)r(r(a) r(b) 1(c))
help_outline

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Let r E S, be any permutation (a b c) e S be any 3-cycle. 72 То prove 7(abe)r(r(a) r(b) 1(c))

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Step 3
(a bc) e S, means
а >ь,ь >сса.So,to show
T(аb c)T* is the 3- сyele
T(а) > T),Г) —т(), T() —Т(а)
help_outline

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(a bc) e S, means а >ь,ь >сса.So,to show T(аb c)T* is the 3- сyele T(а) > T),Г) —т(), T() —Т(а)

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