The following permutation are given in cycle notation. Find their order. (a) f = (1, 2, 3)(4, 5, 7, 6) (b) g = (1, 5, 6, 8, 7)(3, 8, 5, 1, 4, 7)

Part g please

How do you write this as a product of disjoint cycles?

Conjugate elements. Let 0,T E Sn. Define d = TOT. (o and d are called conjugate elements; see Chapter 6.) (a) Show that if o (i) = j, then 8(r (i)) = T(j). (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 8. In other words, if o has cycle decomposition (a1 a2 aki k1)(bị b2 bk2) · ·· . .. ... 3. The Alternating Groups Then d has cycle decomposition (7(a1) T(a2) ·… (c) Illustrate the previous part by letting o = (1 6 3)(7 5 2), and quickly writing down the cycle decomposition for TOT. Check your answer by actually finding the product rOT. T(bk2)) .... (1 4 3 8)(2 6 5), т — T(ak,))(t(b1) T(b2) .. ..