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.

#AbstractAlgebra #GroupTheory #CategoryTheory #Functor #invariant #isomorphism #automorphism

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[Eric-zuiz]

I wish I learned this in my Algebra class this is very interesting!