4. (a) Suppose that τσ=(1 5 2 3)(4) and στ=(1 2 4 5)(3) in S5. If...

4.

(a) Suppose that τσ=(1 5 2 3)(4) and στ=(1 2 4 5)(3) in S5. If σ1 = 2, find σ and τ.

(b) In Sn, show that σ = τ if and only if σ(τ)^(−1) = ε. ε is the identity permutation. Must be written as a proof.

(c) Let σ=(1 2 3) and τ=(1 2) in S3. Show that S3={ε,σ,σ^2,τ,τσ,τ(σ)^2} and that σ^3=ε=τ^2 and στ=τ(σ)^2, then fill out the multiplication table for S3.

Expert Solution

Colby Messinger answered 2 years ago

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