Proof of Cayley's Theorem | Abstract Algebra

Support the production of this course by joining Wrath of Math to access all my Abstract Algebra videos plus lecture notes at the premium tier!    / @wrathofmath   🛍 Check out my math fashion brand! https://mathshion.com/ Abstract Algebra course:    • Abstract Algebra   Abstract Algebra exercises:    • Abstract Algebra Exercises   Get the textbook! https://amzn.to/45IvVgH Business Inquiries: wrathofmathlessons@gmail.com We go over how to prove Cayley's Theorem, which states the incredible fact that every group is isomorphic to some permutation group. This proof will require us to construct a group of permutations of G, then show that G is isomorphic to this permutation. There are a fair bit of details to work out, but it is a surprisingly straightforward proof. #abstractalgebra Permutation Groups:    • Permutation Groups and Symmetric Groups | ...   Isomorphic Groups:    • Isomorphic Groups and Isomorphisms in Grou...   ★DONATE★ ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● TikTok:   / wrathofmathedu   ● X: https://x.com/wrathofmathedu ● Facebook:   / wrathofmath   0:00 Intro 0:48 Constructing Permutations 3:17 Making the Permutation Group 6:23 The Isomorphism 9:02 Conclusion