Lean

• Finite Group Theory
  • Sylow's theorems.
  • Burnside's transfer theorem.
  • The Schur-Zassenhaus theorem.
  • Z-Groups.
  • Schreier's lemma.
  • Commuting probability of finite groups.
• Ring Theory
  • Primary decomposition of modules.
  • Irreducibility of x^n-x-1.
  • Inverse matrices over semirings.
• Field Theory
  • The primitive element theorem.
  • Galois theory.
  • Insolvability of the quintic.
• Number Theory
  • Frobenius elements.
  • L-Functions of elliptic curves.
• Analysis
  • The Pontryagin dual.
• Topology
  • Covering spaces.
• Combinatorics
  • Finite projective planes.