Uploaded October 2018 | Updated September 2026, 3 weeks ago

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Cycle Notation gives you a way to compactly write down a permutation. Since the symmetric group is so important in the study of groups, learning cycle notation will speed up your work with the group Sn. In this lesson we show you how to convert a permutation into cycle notation, talk about the conventions, and discuss the key properties of cycles.

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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
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Milne, Algebra Course Notes (available free online)
jmilne.org/math/CourseNotes/index.html

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Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro
Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison
Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison

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