Abstract Algebra: Isomorphic Groups have Isomorphic Automorphism Groups
Abstract nonsense in the math class Abstract Algebra is fun! If G and Gbar are isomorphic groups, then the group of automorphisms Aut(G) is isomorphic to Aut(Gbar) (so Aut is group invariant for isomorphic groups). How is this proved? Using a simple diagram-chasing argument like in Category Theory. In fact, Aut is an example of a functor in the category of groups from Abstract Algebra.
🔴 "Contemporary Abstract Algebra", by Joe Gallian: https://amzn.to/2ZqLc1J
🔴 Abstract Algebra Exam 1 Review Problems and Solutions: • Abstract Algebra Exam 1 Review Proble...
🔴 Abstract Algebra Exam 2 Review Problems and Solutions: • Abstract Algebra Exam 2 Review Proble...
🔴 Abstract Algebra Exam 3 Review Problems and Solutions: • Abstract Algebra Exam 3 Review Proble...
🔴 Abstract Algebra Final Exam Review Problems and Solutions: • Abstract Algebra Final Exam Review Pr...
🔴 Abstract Algebra Problems with Solutions (including Proofs): • Abstract Algebra Problems with Soluti...
🔴 Abstract Algebra Lectures Playlist: • Abstract Algebra Course, Lecture 1: I...
🔴 Check out my blog at: https://infinityisreallybig.com/
#AbstractAlgebra #GroupTheory #CategoryTheory #Functor #invariant #isomorphism #automorphism
Links and resources
===============================
🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn...
🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/
🔴 Follow me on Twitter: / billkinneymath
🔴 Follow me on Instagram: / billkinneymath
🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA.
🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/
🔴 Desiring God website: https://www.desiringgod.org/
AMAZON ASSOCIATE
As an Amazon Associate I earn from qualifying purchases.