Abstract Algebra 31: How do you write a product of permutations in disjoint cycle notation?

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Abstract Algebra 31: How do you write a product of permutations in disjoint cycle notation?

Abstract: We give two more examples explaining how to write a product of permutations in disjoint cycle notation.

This video accompanies the class "Introduction to Abstract Algebra" at Colorado State University:
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Can you provide the proof this theorem?

sayanjitb