Definition
Subgroup and Normal Subgroup
Let $G$ be a group (Definition~Group (Classical)).
A subset $H \subseteq G$ is a subgroup, written $H \leq G$, if it is closed under multiplication and inverses and contains the identity.
It is normal, written $H \trianglelefteq G$, if $gHg^{-1} = H$ for all $g \in G$.
Depends on
Used in
Dependency Graph
flowchart LR
classDef current fill:#6366f1,color:#fff,stroke:#4f46e5
n71746aac["Group (Classical)"]
n3d67b716["Subgroup and Normal Subgroup"]:::current
n8aabc776["Proposition"]
n4ceac839["Quotient Group"]
n1641e614["Orbit and Stabilizer"]
n28571139["Orbit-Stabilizer Theorem"]
n59ff85d3["Direct and Semidirect Product"]
n738e8542["Universal Cover of a Lie Group"]
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n3d67b716 --> n738e8542
click n71746aac "../objects/71746aac.html" "_self"
click n8aabc776 "../objects/8aabc776.html" "_self"
click n4ceac839 "../objects/4ceac839.html" "_self"
click n1641e614 "../objects/1641e614.html" "_self"
click n28571139 "../objects/28571139.html" "_self"
click n59ff85d3 "../objects/59ff85d3.html" "_self"
click n738e8542 "../objects/738e8542.html" "_self"