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: [email protected] 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
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