Let τ ∈ Sn be the cycle (1, 2, . . . , k) ∈ Sn...

Let τ ∈ S_n be the cycle (1, 2, . . . , k) ∈ S_n where k ≤ n.

(a) For σ ∈ S_n, prove that στσ^-1 = (σ(1), σ(2), . . . , σ(k)).

(b) Let ρ be any cycle of length k in S_n. Prove that there exists an element σ ∈ S_n so that στσ^-1 = ρ.

Expert Solution

Colby Messinger answered 2 years ago

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