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(The “conjugation rewrite lemma”.) Let σ and τ be permutations. (a) Show that if σ maps x...

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Advance Math

(The “conjugation rewrite lemma”.) Let σ and τ bepermutations.

  1. (a) Show that if σ maps x to y then στ maps τ(x) toτ(y).

  2. (b) Suppose that σ is a product of disjoint cycles. Show thatστ has the same cycle structure as

    σ; indeed, wherever (... x y ...) occurs in σ, (... τ(x) τ(y)...) occurs in στ.

Answer & Explanation Solved by verified expert
4.4 Ratings (898 Votes)
a Given that wehaveb Suppose that be a cycle in Thus we    See Answer
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