Theorem

First Isomorphism Theorem

Lie Groups and Lie Algebras · lie-groups.tex

Let $\phi : G \to H$ be a group homomorphism (Definition~Group Homomorphism). Then the quotient group (Definition~Quotient Group) by the kernel (Definition~Kernel and Image) satisfies \[ G / \ker\phi \;\cong\; \operatorname{im}\phi. \]

Depends on

Group Homomorphism
Quotient Group
Kernel and Image

Dependency Graph

flowchart LR classDef current fill:#6366f1,color:#fff,stroke:#4f46e5 ne087180c["Group Homomorphism"] n4ceac839["Quotient Group"] n6fd9cebe["Kernel and Image"] n856a1ed3["First Isomorphism Theorem"]:::current ne087180c --> n856a1ed3 n4ceac839 --> n856a1ed3 n6fd9cebe --> n856a1ed3 click ne087180c "../objects/e087180c.html" "_self" click n4ceac839 "../objects/4ceac839.html" "_self" click n6fd9cebe "../objects/6fd9cebe.html" "_self"