definition 4.45 Group automorphism

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:1567 · p. 76

ground object -- no derivation owed

Rests on

depends_on definition 4.44 Group isomorphism ¶
- depends_on definition 4.43 Group homomorphism ¶
  - depends_on definition 4.21 Group ¶
    - depends_on definition 4.11 Inverse element ¶
      - depends_on definition 4.9 Neutral element ¶
    - depends_on definition 4.20 Monoid ¶
      - depends_on definition 4.9 Neutral element ¶ ↺
      - depends_on definition 4.18 Semigroup ¶
  - depends_on definition 3.43 Map ¶
    - depends_on definition 3.24 Quantifiers ¶
      - depends_on definition 3.23 Predicate ¶
    - depends_on definition 3.28 Set ¶
- depends_on definition 3.47 Bijective map ¶

Supports

depends_on proposition 4.72 The automorphism group ¶
- 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      - depends_on remark 18.22 Superseded, and in exactly what sense ¶
  - 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 proposition 18.20 The Galilean group ¶ ↺
  - depends_on theorem 4.76 Internal characterization of the semidirect product ¶

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 isomorphism	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1572
`depends_on`	←	The automorphism group	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2656