Group Theory
In order to advance my understanding of group theory, I am writing down and proving the first couple of chapters of Dummit and Foote's "Abstract Algebra" textbook in the automated theorem prover Lean.
So far, here are all the things I have formalized
- the definition of a group
- the defintiion of an abelian group
- propositions about groups, e.g. for all a, -(-a) = a
- proof that integers under additon are a group
- proof that rationals under addition are a group
- proof that the dihedral group is a group
- proof that the symmetric group is a group
- defintion of a homomorphism
- definition of an isomorphism
I welcome all pull requests.