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Symmetric Groups (Abstract Algebra)

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Published on Sep 9, 2014

Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n.

Symmetric groups capture the history of abstract algebra, provide a wide range of examples in group theory, are useful when writing software to study abstract algebra, and every finite group can be represented as a subgroup of a symmetric group. This result is known as Cayley's Theorem.

Order of an Element Video: https://www.youtube.com/watch?v=OWTKY...

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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
http://amzn.to/2oOBd5S

Milne, Algebra Course Notes (available free online)
http://www.jmilne.org/math/CourseNote...

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

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