proposition 4.72 The automorphism group
open in the book ·
parts/02-mathematical-methods/02-algebraic-structures.tex:2651
· p. 90
Rests on
-
depends_on
definition 4.45
Group automorphism
¶
-
depends_on
definition 4.44
Group isomorphism
¶
- depends_on definition 4.43 Group homomorphism ¶
- depends_on definition 3.47 Bijective map ¶
-
depends_on
definition 4.44
Group isomorphism
¶
- depends_on definition 4.36 Subgroup ¶
-
depends_on
definition 4.48
Symmetric group
¶
- depends_on definition 3.47 Bijective map ¶ ↺
- proves proof ch:02-algebraic-structures@proof-27 ¶
Supports
-
depends_on
definition 4.73
External semidirect product
¶
-
depends_on
example 4.78
The Euclidean group
¶
-
depends_on
proposition 18.20
The Galilean group
¶
-
depends_on
corollary 18.24
Galilean composition of velocities
¶
- depends_on phenomenon 18.26 Composition of velocities, and its limit ¶
- depends_on remark 18.25 Where the additivity goes ¶
- depends_on remark 18.22 Superseded, and in exactly what sense ¶
-
depends_on
corollary 18.24
Galilean composition of velocities
¶
-
depends_on
proposition 18.20
The Galilean group
¶
- depends_on example 4.79 The Poincaré group ¶
-
depends_on
proposition 4.74
The semidirect product is a group
¶
-
depends_on
proposition 4.75
The two factors inside the semidirect product
¶
- depends_on example 4.79 The Poincaré group ¶ ↺
-
depends_on
proposition 4.77
When a semidirect product is direct
¶
- depends_on example 4.78 The Euclidean group ¶ ↺
-
depends_on
proposition 4.75
The two factors inside the semidirect product
¶
- depends_on proposition 18.20 The Galilean group ¶ ↺
- depends_on theorem 4.76 Internal characterization of the semidirect product ¶
-
depends_on
example 4.78
The Euclidean group
¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Group automorphism | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:2656 |
depends_on |
→ | Subgroup | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:2656 |
depends_on |
→ | Symmetric group | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:2656 |
depends_on |
← | External semidirect product | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:2692 |
proves |
← | ch:02-algebraic-structures@proof-27 | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:2659 |