Definition
Group (Classical)
A group is a pair $(G,\cdot)$ consisting of a set $G$ together with a binary operation
\[
\cdot : G \times G \to G
\]
such that:
- Associativity: For all $a,b,c \in G$, $(a \cdot b)\cdot c = a \cdot (b \cdot c)$.
- Identity: There exists an element $e \in G$ such that for all $a \in G$, $e \cdot a = a \cdot e = a$.
- Inverses: For every $a \in G$, there exists $a^{-1} \in G$ such that $a \cdot a^{-1} = a^{-1} \cdot a = e$.
Used in
Dependency Graph
flowchart LR
classDef current fill:#6366f1,color:#fff,stroke:#4f46e5
n3d67b716["Subgroup and Normal Subgroup"]
ne83c1383["Character"]
n71746aac["Group (Classical)"]:::current
ne087180c["Group Homomorphism"]
nf7184fc4["Group Action"]
nca6bd350["Representation"]
n4cacdd3e["Group (Categorical)"]
n59ff85d3["Direct and Semidirect Product"]
ne5f4203c["Lie Group"]
n71746aac --> n4cacdd3e
n71746aac --> ne087180c
n71746aac --> n3d67b716
n71746aac --> nf7184fc4
n71746aac --> n59ff85d3
n71746aac --> nca6bd350
n71746aac --> ne83c1383
n71746aac --> ne5f4203c
click n3d67b716 "../objects/3d67b716.html" "_self"
click ne83c1383 "../objects/e83c1383.html" "_self"
click ne087180c "../objects/e087180c.html" "_self"
click nf7184fc4 "../objects/f7184fc4.html" "_self"
click nca6bd350 "../objects/ca6bd350.html" "_self"
click n4cacdd3e "../objects/4cacdd3e.html" "_self"
click n59ff85d3 "../objects/59ff85d3.html" "_self"
click ne5f4203c "../objects/e5f4203c.html" "_self"