First: G/ker φ ≅ im φ for any homomorphism φ. Second: (HN)/N ≅ H/(H∩N) when N normal. Third: (G/N)/(K/N) ≅ G/K when N ⊆ K, both normal. Formalises the quotient/substructure interplay.
Isomorphism theorems (groups/rings/modules)
Related concepts
- Quotient group
- Group homomorphism
- Cartan classification of simple Lie algebras
- Highest weight rep (cross-listed L0 lie-theory)
- Łoś ultraproduct theorem
- Nonstandard analysis (Robinson)
- Morley categoricity theorem
- Zilber-Hrushovski geometry of strongly-minimal sets
- Curry-Howard correspondence
- Modularity theorem (Wiles / Fermat)
- Identity type (Id)
- Exterior derivative d
- Poincare duality (cohomology)
- Hahn-Banach extension theorem (1929)
- Uniform boundedness (Banach-Steinhaus)
- Open mapping theorem (Banach 1929)
- Closed graph theorem
- Godel Dialectica translation
- Frobenius reciprocity
- Homotopy equivalence (detail)