Symmetric Groups (Abstract Algebra)

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:    • The Order of an Element  (Abstract Algebra)   Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ 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... ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon :   / socratica   ► Make a one-time PayPal donation: https://www.paypal.me/socratica ► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank you! ♦♦♦♦♦♦♦♦♦♦ Connect with us! Facebook:   / socraticastudios   Instagram:   / socraticastudios   Twitter:   / socratica   ♦♦♦♦♦♦♦♦♦♦ Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison ♦♦♦♦♦♦♦♦♦♦