Determining the elements of the subgroups, Algebra

Determining the elements of the subgroups

Assignment: Let σ = (1 3 5 7) and τ = (2 7 3) be elements of S7.

Q1. Find all elements of the subgroups (σ) and (τ).

Q2. What order does σ have? What order does τ have? Can you generalize this to a statement for any cycle?

Q3. Compute the product στ. What is its order?

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