definition 4.67 Product of subgroups

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:2435 · p. 88

ground object -- no derivation owed

Rests on

depends_on definition 4.36 Subgroup ¶
- 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 ¶

Supports

depends_on proposition 4.70 Characterization of the direct product ¶
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 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      - depends_on remark 18.22 Superseded, and in exactly what sense ¶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 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`	→	Subgroup	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2441
`depends_on`	←	Characterization of the direct product	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2541
`depends_on`	←	The two factors inside the semidirect product	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2786
`depends_on`	←	Internal characterization of the semidirect product	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2848