definition 4.44 Group isomorphism

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:1490 · p. 76

ground object -- no derivation owed

Rests on

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 4.3 Algebraic structure ¶
  - depends_on definition 4.20 Monoid ¶
    - depends_on definition 4.9 Neutral element ¶ ↺
    - depends_on definition 4.18 Semigroup ¶
      - depends_on definition 4.6 Associativity ¶
      - depends_on definition 4.4 Internal binary operation; magma ¶
- depends_on definition 3.43 Map ¶
  - depends_on definition 3.24 Quantifiers ¶
    - depends_on definition 3.23 Predicate ¶
      - depends_on definition 3.1 Logical proposition ¶
      - depends_on definition 3.38 Ordered pair and Cartesian product ¶
  - depends_on definition 3.28 Set ¶
depends_on definition 3.47 Bijective map ¶

Supports

depends_on definition 4.45 Group automorphism ¶
- 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 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 proposition 18.20 The Galilean group ¶ ↺
    - depends_on theorem 4.76 Internal characterization of the semidirect product ¶
depends_on definition 5.143 Faithful representation ¶
depends_on proposition 4.70 Characterization of the direct product ¶
depends_on proposition 4.55 $S_3$ and the equilateral triangle ¶
depends_on theorem 4.56 Cayley's theorem ¶

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 homomorphism	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1495
`depends_on`	→	Bijective map	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1495
`depends_on`	←	Group automorphism	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1572
`depends_on`	←	Faithful representation	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:6223
`depends_on`	←	Characterization of the direct product	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2541
`depends_on`	←	$S_3$ and the equilateral triangle	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1911
`depends_on`	←	Cayley's theorem	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1948